• 제목/요약/키워드: Characteristic ring-modules

검색결과 6건 처리시간 0.02초

SOME PROPERTIES ON THE CHARACTERISTIC RING-MODULES

  • PARK CHIN HONG;LIM JONG SEUL
    • Journal of applied mathematics & informatics
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    • 제17권1_2_3호
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    • pp.771-778
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    • 2005
  • In this paper we shall give some group properties derived from the characteristic ring-module $_X(M)$, using the fact that $_X(M)_H$ is a conjugate to $_X(M)_{Ha}$ when M is an invertible right R-module. Also we shall prove that_X(M)$ is group-isomorphic to TR and some normal subgroup properties if M is invertible and R is commutative.

Multiplication Modules and characteristic submodules

  • Park, Young-Soo;Chol, Chang-Woo
    • 대한수학회보
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    • 제32권2호
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    • pp.321-328
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    • 1995
  • In this note all are commutative rings with identity and all modules are unital. Let R be a ring. An R-module M is called a multiplication module if for every submodule N of M there esists an ideal I of R such that N = IM. Clearly the ring R is a multiplication module as a module over itself. Also, it is well known that invertible and more generally profective ideals of R are multiplication R-modules (see [11, Theorem 1]).

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ON THE CHARACTERISTIC RING-MODULES

  • Park, Chin-Hong
    • 대한수학회보
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    • 제32권2호
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    • pp.145-152
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    • 1995
  • From now on, we assume that a ring R has an identity 1. We have the following Lemma from Park[2].

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Certain exact complexes associated to the pieri type skew young diagrams

  • Chun, Yoo-Bong;Ko, Hyoung J.
    • 대한수학회보
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    • 제29권2호
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    • pp.265-275
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    • 1992
  • The characteristic free representation theory of the general linear group has found a wide range of applications, ranging from the theory of free resolutions to the symmetric function theory. Representation theory is used to facilitate the calculation of explicit free resolutions of large classes of ideals (and modules). Recently, K. Akin and D. A. Buchsbaum [2] realized the Jacobi-Trudi identity for a Schur function as a resolution of GL$_{n}$-modules. Over a field of characteristic zero, it was observed by A. Lascoux [6]. T.Jozefiak and J.Weyman [5] used the Koszul complex to realize a formula of D.E. Littlewood as a resolution of schur modules. This leads us to further study resolutions of Schur modules of a particular form. In this article we will describe some new classes of finite free resolutions associated to the Pieri type skew Young diagrams. As a special case of these finite free resolutions we obtain the generalized Koszul complex constructed in [1]. In section 2 we review some of the basic difinitions and properties of Schur modules that we shall use. In section 3 we describe certain exact complexes associated to the Pieri type skew partitions. Throughout this article, unless otherwise specified, R is a commutative ring with an identity element and a mudule F is a finitely generated free R-module.e.

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CAUCHY DECOMPOSITION FORMULAS FOR SCHUR MODULES

  • Ko, Hyoung J.
    • 대한수학회보
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    • 제29권1호
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    • pp.41-55
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    • 1992
  • The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

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Minimal Generators of Syzygy Modules Via Matrices

  • Haohao Wang;Peter Oman
    • Kyungpook Mathematical Journal
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    • 제64권2호
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    • pp.197-204
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    • 2024
  • Let R = 𝕂[x] be a univariate polynomial ring over an algebraically closed field 𝕂 of characteristic zero. Let A ∈ Mm,m(R) be an m×m matrix over R with non-zero determinate det(A) ∈ R. In this paper, utilizing linear-algebraic techniques, we investigate the relationship between a basis for the syzygy module of f1, . . . , fm and a basis for the syzygy module of g1, . . . , gm, where [g1, . . . , gm] = [f1, . . . , fm]A.