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The socle of the last term in a minimal injective resolution

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Science China Mathematics 2010年第7期53卷 1714-1720页

作者： Huang ZhaoYong Wang Yao Nanjing Univ Dept Math Nanjing 210093 Peoples R China Nanjing Univ Informat Sci & Technol Coll Math & Phys Nanjing 210044 Peoples R China

Let Λ and Γ be left and right Noetherian rings and Λ U a generalized tilting module with Γ = End( Λ U ). For a non-negative integer k, if Λ U is (k - 2)-Gorenstein with the injective dimensions of Λ U and U Γ ... 详细信息

关键词： generalized tilting modules (quasi) k-Gorenstein modules socle minimal injective resolution injective dimension

DIMENSION VECTOR,LOEWY FACTORS,socle FACTORS ARE THE INVARIANTS OF AUSLANDER-REITEN QUIVERS

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Chinese Science Bulletin 1992年第10期37卷 793-797页

作者：邓邦明肖杰 Department of Mathematics Beijing Normal University Beijing 100875 PRC Department of Mathematics Beijing Normal University Beijing 100875 PRC Let k be an algebraically closed field ∧a finite dimensional k-algebra. According to Morita equivalence we can always assume that ∧is basic and connected. We denote by mod∧the category of all finite generated left ∧-modules and by F_∧the Auslander-Reiten quiver of A. Let P_1 P_2… P_n be all the indecomposable projective modules up to isomorphism. For any module M ∈mod∧ its dimension vector is defined by

Let k be an algebraically closed field, ∧ a finite dimensional k-algebra. According to Morita equivalence, we can always assume that ∧ is basic and connected. We denote by mod∧ the category of all finite generated left ∧-modules, and by F∧ the Auslander-Reiten quiver of A. Let P1, P2,…, Pn be all the indecomposable projective modules up to isomorphism. For any module M ∈ mod∧, its dimension vector is defined

关键词： dimension vector Loewy factors socle factors covering functor k-category

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环的socle与同调维数

南京大学学报（数学半年刊） 1993年第1期10卷 89-92页

作者：杨静化

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环的本质理想和socle

江西教育学院学报 1989年第4期10卷 51-56页

作者：余承友

[1]定义了模的本质子模和SocIe,并以此研究模的结构,得到了许多好的结果。一般说通过环与环上模的内在联系研究环与模的结构是一个常用的有效方法。本文尝试借用模的研究方法来研究环的结构,在环中定义本质理想和环的socle,并以此得到... 详细信息

[1]定义了模的本质子模和SocIe,并以此研究模的结构,得到了许多好的结果。一般说通过环与环上模的内在联系研究环与模的结构是一个常用的有效方法。本文尝试借用模的研究方法来研究环的结构,在环中定义本质理想和环的socle,并以此得到本质理想的一些性质及Soc 理想可升环的socle 的内刻化定理。

关键词：本质理想环的 socle

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半径Banach代数socle的存在性

Journal of Mathematical Research with Applications 1986年第3期 23-26页

作者：杨庆德云南工学院

1975年***、***引进径Banach代数的概念,此类代数包含全体队代数和***的算子理想。在[1]中,作者们得到的主要结果之一是:每个弱紧的径Banach代数的socle存在。1978年***引进半径Banach代数的概念,并且证明了这类代数严格包含径Banach代... 详细信息

1975年***、***引进径Banach代数的概念,此类代数包含全体队代数和***的算子理想。在[1]中,作者们得到的主要结果之一是:每个弱紧的径Banach代数的socle存在。1978年***引进半径Banach代数的概念,并且证明了这类代数严格包含径Banach代数类。在本文中,我们证明了每个弱紧半径Banach代数的socle仍然存在,此外,本文还给出了把一个不带单位元的半径Banach代数同胚地嵌入到一个带单位元的半径Banach代数中去的条件,以及一个紧半径Banach代数是有限维的条件。

关键词： socle Banach 代数初等数学幂等元

Commutators with Finite Spectrum Ⅱ

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Acta Mathematica Sinica,English Series 2009年第5期25卷 815-830页

作者： Nadia BOUDI Département

The purpose of this paper is to study derivations d, d′ defined on a Banach algebra A such that the spectrum a（[dx, d′x]） is finite for all x ∈ A. In particular we show that if the algebra is semisimple, then the... 详细信息

关键词： Banach algebras derivations commutators finite spectra socle

AN EFFECTIVE CRITERION FOR UNIQUENESS OF THE TILTING MODULE

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Chinese Science Bulletin 1992年第18期37卷 1508-1511页

作者：林亚南彭联刚 Department of Mathematics Beijing Normal University Beijing 100875 PRC

Throughout this note, we assume that k is an algebraically closed field and A is a basic connected finite-dimensional algebra over k (associative, with identity). All modules over an algebra A are finitely generated left A-modules. We usually denote, up to isomorphism, by {P_A(a)|a∈I} the set of all indecomposable projective modules, by {E_A(a)|a∈I} the set of all indecomposable injective modules, and by {S_A(a)|a∈I} the set of all simple modules,

关键词： tilting module top socle ordinary quiver of algebra.

Orthogonality of the idempotent elements with rank one in primitive rings

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Science China Mathematics 1996年第6期39卷 598-603页

作者：蒋滋梅 Department of Mathematics Beijing Normal University Beijing 100875 China

Let R be a primitive ring with nonzero socle, M a faithful irreducible right R-module, A the central-izer of M, and L= a direct sum of countably many minimal right ideals L, of R. Then there existsa family of subsetsis infinite) of R such that L=R for any W, whereeach is a set of countably many orthogonal idempotent elements of rank one in R. Furthermore,there exists a primitive ring R and a direct sum L=of countably many minimal right ideals Li ofR, but R has no subset B =of countably many orthogonal idempotent elements of rank one such that and B can be extended to a corresponding basis of some basis of M over A.

关键词： primitive ring socle conjugate space idempotent element of rank one.

The Second Hochschild Cohomology Group for One-Parametric Self-Injective Algebras

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Advances in Pure Mathematics 2013年第5期3卷 458-469页

作者： Deena Al-Kadi Department of Mathematics Taif University Taif KSA

In this paper, we determine the second Hochschild cohomology group for a class of self-injective algebras of tame representation type namely, which are standard one-parametric but not weakly symmetric. These were classified up to derived equivalence by Bocian, Holm and Skowroński in [1]. We connect this to the deformation of these algebras.

关键词： Hochschild Cohomology Self-Injective Algebras socle Deformation