Updated on 2024/12/21

写真a

 
HARIMA Tadahito
 
Organization
Academic Assembly Institute of Humanities and Social Sciences KYOIKUGAKU KEIRETU Professor
Graduate School of Education School Subjects Professor
Faculty of Education Mathematical and Natural Sciences Professor
Title
Professor
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Degree

  • 博士（理学） ( 1998.3   広島大学 )

Research Interests

  • ・ゴレンスタイン環のヒルベルト関数とベッチ数列の特徴付け問題 ・レベル環のヒルベルト関数とベッチ数列の特徴付け問題 ・完全交叉のレフシェッツ性問題 ・単項式イデアルのジェネリックイニシャルイデアルに関する研究

Research History (researchmap)

  • - 愛媛大学教育学部

    2009

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  • Hokkaido University of Education

    2007 - 2009

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  • Hokkaido University of Education

    2004 - 2007

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  • Shikoku University   Faculty of Management and Information Science

    2000 - 2004

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  • Shikoku University   Faculty of Management and Information Science

    1995 - 2000

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  • Shikoku University   Faculty of Management and Information Science

    1993 - 1995

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  • Niigata University Faculty of Education, Chair of Mathematical and Natural Sciences

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  • Ehime University Faculty of Education, Faculty of Education   Associate Professor

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Research History

  • Niigata University   Faculty of Education Mathematical and Natural Sciences   Professor

    2013.4

  • Niigata University   Graduate School of Education School Subjects   Professor

    2013.4

Education

  • Hiroshima University   理学研究科

    - 1993

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    Country： Japan

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  • Hiroshima University   Graduate School, Division of Natural Science

    - 1993

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  • Hiroshima University   理学研究科

    - 1990

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    Country： Japan

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  • Hiroshima University   Graduate School, Division of Natural Science

    - 1990

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  • Kochi University   理学部   数学科

    - 1987

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    Country： Japan

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  • Kochi University   Faculty of Science

    - 1987

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Professional Memberships

 

MISC

  • Generic initial ideals of some monomial complete intersections in four variables

    Tadahito Harima, Sho Sakaki, Akihito Wachi

    ARCHIV DER MATHEMATIK   94 ( 2 )   129 - 137   2010.2

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    Language：English   Publisher：BIRKHAUSER VERLAG AG  

    Let R = K[x(1), x(2), x(3), x(4)] be the polynomial ring over a field of characteristic zero. For the ideal (x(1)(a), x(2)(b), x(3)(c), x(4)(d)) subset of R, where at least one of a, b, c and d is equal to two, we prove that its generic initial ideal with respect to the reverse lexicographic order is the almost revlex ideal corresponding to the same Hilbert function.

    DOI： 10.1007/s00013-009-0088-2

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  • GENERIC INITIAL IDEALS, GRADED BETTI NUMBERS, AND k-LEFSCHETZ PROPERTIES

    Tadahito Harima, Akihito Wachi

    COMMUNICATIONS IN ALGEBRA   37 ( 11 )   4012 - 4025   2009

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    Language：English   Publisher：TAYLOR & FRANCIS INC  

    We introduce the k-strong Lefschetz property and the k-weak Lefschetz property for graded Artinian K-algebras, which are generalizations of the Lefschetz properties. The main results are:
    1. Let I be an ideal of R = K[x(1), x(2), ..., x(n)] whose quotient ring R/I has the n-SLP. Suppose that all kth differences of the Hilbert function of R/I are quasi-symmetric. Then the generic initial ideal of I is the unique almost revlex ideal with the same Hilbert function as R/I.
    2. We give a sharp upper bound on the graded Betti numbers of Artinian K-algebras with the k-WLP and a fixed Hilbert function.

    DOI： 10.1080/00927870802502753

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  • The commutator algebra of a nilpotent matrix and an application to the theory of commutative Artinian algebras

    Tadahito Harima, Junzo Watanabe

    JOURNAL OF ALGEBRA   319 ( 6 )   2545 - 2570   2008.3

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    Language：English   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    We show a number of properties of the commutator algebra of a nilpotent matrix over a field. In particular we determine the simple modules of the commutator algebra. Then the results are applied to prove that certain Artinian complete intersections have the strong Lefschetz property. (C) 2007 Elsevier Inc. All tights reserved.

    DOI： 10.1016/j.jalgebra.2007.09.011

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  • 割り算への誘（いざな）い

    日本数学教育学会誌（算数教育57－2）   90 ( 4 )   58 - 66   2008

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  • The central simple modules of Artinian Gorenstein algebras

    Tadahito Harima, Junzo Watanabe

    JOURNAL OF PURE AND APPLIED ALGEBRA   210 ( 2 )   447 - 463   2007.8

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    Language：English   Publisher：ELSEVIER SCIENCE BV  

    Let A be a standard graded Artinian K-algebra, with char K = 0. We prove the following.
    1. A has the Weak Lefschetz Property (resp. Strong Lefschetz Property) if and only if Gr((z)) (A) has the Weak Lefschetz Property (resp. Strong Lefschetz Property) for some linear form z of it. 2. If A is Gorenstein, then A has the Strong Lefschetz Property if and only if there exists a linear form z of A such that all central simple modules of (A, z) have the Strong Lefschetz Property.
    As an application of these theorems, we give some new classes of Artinian complete intersections with the Strong Lefschetz Property. (C) 2006 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.jpaa.2006.10.016

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  • The strong Lefschetz property for Artinian algebras with non-standard grading

    Tadahito Harima, Junzo Watanabe

    JOURNAL OF ALGEBRA   311 ( 2 )   511 - 537   2007.5

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    Language：English   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let A = circle plus(c)(i=0) A(i) be a graded Artinian K-algebra, where A(c) not equal (0) and char K = 0. (The grading may not necessarily be standard.) Then A has the strong Lefschetz property if there exists an element g is an element of A(1) such that the multiplication x g(c-2i) : A(i) -> A(c-i) is bijective for every i = 0, 1, . . . , [c/2]. The main results obtained in this paper are as follows:
    1. A has the strong Lefschetz property if and only if there is a linear form z is an element of A(1) such that Gr((z))(A) has the strong Lefschetz property.
    2. If A is Gorenstein, then A has the strong Lefschetz property if and only if there is a linear form z is an element of A such that all central simple modules of (A, z) have the strong Lefischetz property.
    3. A finite free extension of an Artinian K-algebra with the strong Lefschetz property has the strong Lefschetz property if the fiber does.
    4. The complete intersection defined by power sums of consecutive degrees has the strong Lefschetz property. (c) 2007 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jalgebra.2007.01.019

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  • The Hilbert function of a level algebra

    Memoirs of the American Mathematical Society   186 ( 872 )   1 - 139   2007

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  • The Hilbert function of a level algebra

    Memoirs of the American Mathematical Society   186 ( 872 )   1 - 139   2007

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  • Some special configurations of points in P-n

    AV Geramita, T Harima, YS Shin

    JOURNAL OF ALGEBRA   268 ( 2 )   484 - 518   2003.10

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    Language：English   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    DOI： 10.1016/S0021-8693(03)00118-2

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  • Some special configurations of points in P-n

    AV Geramita, T Harima, YS Shin

    JOURNAL OF ALGEBRA   268 ( 2 )   484 - 518   2003.10

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    Language：English   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    DOI： 10.1016/S0021-8693(03)00118-2

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  • The Weak and Strong Lefschetz properties for Artinian K-algebras

    T Harima, JC Migliore, U Nagel, J Watanabe

    JOURNAL OF ALGEBRA   262 ( 1 )   99 - 126   2003.4

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    Language：English   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let A = circle plus(igreater than or equal to0) A(i) be a standard graded Artinian K-algebra, where char K = 0. Then A has the Weak Lefschetz property if there is an element iota of degree 1 such that the multiplication x iota: A(i) --> A(i+1) has maximal rank, for every i, and A has the Strong Lefschetz property if x iota(d) : A(i) --> A(i+d) has maximal rank for every i and d. The main results obtained in this paper are the following.
    (1) Every height-three complete intersection has the Weak Lefschetz property. (Our method, surprisingly, uses rank-two vector bundles on P-2 and the Grauert-Mulich theorem.)
    (2) We give a complete characterization (including a concrete construction) of the Hilbert functions that can occur for K-algebras with the Weak or Strong Lefschetz property (and the characterization is the same one!).
    (3) We give a sharp bound on the graded Betti numbers (achieved by our construction) of Artinian K-algebras with the Weak or Strong Lefschetz property and fixed Hilbert function. This bound is again the same for both properties! Some Hilbert functions in fact force the algebra to have the maximal Betti numbers. (4) Every Artinian ideal in K[x, y] possesses the Strong Lefschetz property. This is false in higher codimension. (C) 2003 Elsevier Science (USA). All rights reserved.

    DOI： 10.1016/S0021-8693(03)00038-3

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  • The finite free extension of ArtinianK-algebras with the strong Lefschetz property

    The Rendiconti del Seminario Matematico di Padova   110   1 - 29   2003

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  • The finite free extension of ArtinianK-algebras with the strong Lefschetz property

    The Rendiconti del Seminario Matematico di Padova   110   1 - 29   2003

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  • On Hilbert functions and Betti numbers of some Artinian Gorenstein rings

    Queen's Papers in Pure and Applied Mathematics (Queen's University, Canada)   123   B1-B11   2002

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  • On Hilbert functions and Betti numbers of some Artinian Gorenstein rings

    Queen's Papers in Pure and Applied Mathematics (Queen's University, Canada)   123   B1-B11   2002

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  • Decompositions of the Hilbert function of a set of points in P-n

    AV Geramita, T Harima, YS Shin

    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES   53 ( 5 )   923 - 943   2001.10

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    Language：English   Publisher：CANADIAN MATHEMATICAL SOC  

    Let H be the Hilbert function of some set of distinct points in P-n and let alpha = alpha (H) be the least degree of a hypersurface of P-n containing these points. Write alpha = d(s) + d(s-1) +...+ d(1) (where d(i) > 0). We canonically decompose H into s other Hilbert functions H <----> (H-s',...,H-1') and show how to find sets of distinct points Y-s,..., Y-1, lying on reduced hypersurfaces of degrees d(s),...,d(1) (respectively) such that the Hilbert function of Y-i is H-i' and the Hilbert function of Y = boolean OR (s)(i=1) Y-i is H. Some extremal properties of this canonical decomposition are also explored.

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  • An alternetive to the Hilbert function for the ideal of a finite set of points in P^ｎ

    Illinois Journal of Mathematics   45 ( 1 )   1 - 23   2001

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  • An alternetive to the Hilbert function for the ideal of a finite set of points in P^ｎ

    Illinois Journal of Mathematics   45 ( 1 )   1 - 23   2001

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  • Extremal point sets and Gorenstein ideals

    AV Geramita, T Harima, YS Shin

    ADVANCES IN MATHEMATICS   152 ( 1 )   78 - 119   2000.6

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    Language：English   Publisher：ACADEMIC PRESS INC  

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  • A note on Artinian Gorenstein algebras of codimension three

    T Harima

    JOURNAL OF PURE AND APPLIED ALGEBRA   135 ( 1 )   45 - 56   1999.2

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    Language：English   Publisher：ELSEVIER SCIENCE BV  

    In this paper, using a standard fact in linkage theory, we give a new construction of Artinian Gorenstein algebras achieving all possible sets of graded Betti numbers for codimension three. Furthermore, as an application, we give another proof of Stanley's well-known characterization theorem for the Hilbert functions of codimension three Artinian Gorenstein algebras. (C) 1999 Elsevier Science B.V. All rights reserved.

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  • A note on Artinian Gorenstein algebras of codimension three

    Journal of Pure and Applied Algebra   135 ( 1 )   45 - 56   1999

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  • SOME EXAMPLES OF UNIMODAL GORENSTEIN SEQUENCES

    T HARIMA

    JOURNAL OF PURE AND APPLIED ALGEBRA   103 ( 3 )   313 - 324   1995.9

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    Language：English   Publisher：ELSEVIER SCIENCE BV  

    We study h-sequences of certain Gorenstein standard G-algebras and, for a given SI-sequence ($) under bar h = (h(1),..., h(s)) with h(1) = 3, give a new construction of Gorenstein standard G-algebras with h-sequence ($) under bar h. Furthermore, using a similar idea, we give some examples of Gorenstein SI-sequenceswith h(1) = 4.

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  • Characterization of Hilbert functions of Gorenstein Artin algebras with the weak Stanley property

    Proceedings of the American Mathematical Society   123 ( 12 )   313 - 324   1995

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  • A formulation of Quantum Turing Machine

    4 ( 4 )   1 - 8   1995

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  • Notes on Computational Complexity Theory

    3 ( 3 )   7 - 24   1995

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  • Some examples of unimodal Gorenstein sequences

    Journal of Pure and Applied Algebra   103 ( 3 )   313 - 324   1995

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  • Characterization of Hilbert functions of Gorenstein Artin algebras with the weak Stanley property

    Proceedings of the American Mathematical Society   123 ( 12 )   313 - 324   1995

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  • A formulation of Quantum Turing Machine

    Bulletin of Shikoku University   4 ( 4 )   1 - 8   1995

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  • Notes on computational complexity theory

    Bulletin of Shikoku University   3 ( 3 )   7 - 24   1995

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  • The conductor of some special points in P^2

    Journal of Mathematics (Tokushima University)   28   5 - 18   1994

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  • On the theory of Computability

    2 ( 2 )   1 - 18   1994

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  • On the theory of computability

    Bulletin of Shikoku University   2   1 - 18   1994

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  • The conductor of some special points in P^2

    Journal of Mathematics (Tokushima University)   28   5 - 18   1994

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  • On the lifting problem for complete intersection homogeneous ideals in polynomial rings

    Queen's Papers in Pure and Applied Mathematics （Queen's University, Canada）   95   D1-D5   1993

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  • On the lifting problem for complete intersection homogeneous ideals in polynomial rings

    Queen's Papers in Pure and Applied Mathematics （Queen's University, Canada）   95   D1-D5   1993

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Research Projects

  • 完全交叉のレフシェッツ性問題と単項式イデアルのジェネリックイニシャルイデアルに関する研究

    2004

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    Grant type：Competitive

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Teaching Experience

  • 代数学特講

    2022
    Institution name：新潟大学

  • 代数学講義II

    2022
    Institution name：新潟大学

  • 数学・数学教育学研究入門

    2021
    -
    2023
    Institution name：新潟大学

  • 教育実践体験研究IV

    2021
    Institution name：新潟大学

  • 教育実践体験研究II

    2021
    Institution name：新潟大学

  • 教育実践体験研究I

    2021
    Institution name：新潟大学

  • 教育実践体験研究III

    2021
    Institution name：新潟大学

  • 代数学講義I

    2021
    Institution name：新潟大学

  • 微分積分学I

    2020
    Institution name：新潟大学

  • 線形代数学II

    2018
    Institution name：新潟大学

  • 線形代数学I

    2018
    Institution name：新潟大学

  • 可換環論

    2017
    Institution name：新潟大学

  • 小学校算数

    2015
    Institution name：新潟大学

  • 代数学序説

    2015
    -
    2017
    Institution name：新潟大学

  • くらしと数理

    2015
    Institution name：新潟大学

  • スタディ・スキルズH

    2014
    Institution name：新潟大学

  • 代数学講義II

    2014
    -
    2022
    Institution name：新潟大学

  • 代数学講義I

    2014
    -
    2021
    Institution name：新潟大学

  • 数学科教材開発研究特論

    2014
    -
    2016
    Institution name：新潟大学

  • 解析学特講

    2014
    Institution name：新潟大学

  • 代数系の基礎I

    2013
    Institution name：新潟大学

  • 卒業研究

    2013
    Institution name：新潟大学

  • 代数系の基礎II

    2013
    Institution name：新潟大学

  • 応用代数学II

    2013
    -
    2017
    Institution name：新潟大学

  • 代数学課題研究III

    2013
    -
    2016
    Institution name：新潟大学

  • 代数学課題研究IV

    2013
    -
    2016
    Institution name：新潟大学

  • 代数学特論I

    2013
    -
    2016
    Institution name：新潟大学

  • 代数学課題研究II

    2013
    -
    2015
    Institution name：新潟大学

  • 応用代数学I

    2013
    -
    2015
    Institution name：新潟大学

  • 代数学演習I

    2013
    -
    2015
    Institution name：新潟大学

  • 代数学課題研究I

    2013
    -
    2015
    Institution name：新潟大学

  • 数と規則性II

    2013
    Institution name：新潟大学

  • 数と規則性I

    2013
    Institution name：新潟大学

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