单项代数的一个注记

本文研究单项代数上模的同调性质.应用Huisgen-Zimmermann的著名结果,分别给出了由一条道路生存的投射模及好模存在的充分条件.     

Gorenstein Cotilting and Tilting Modules

Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting modules in relative homological algebra considering subfunctors of the Ext-functor. In this article we generalize Auslander–Solberg relative notions by giving the definitions of infinitely generated Gorenstein cotilting and tilting modules by means of Gorenstein exact sequences. Using the theory developed by Enochs on the existence of Gorenstein preenvelopes and precovers, we prove a characterization of relative Gorenstein cotilting and tilting modules, which is a generalization of the beautiful characterization of relative cotilting and tilting modules given by Bazzoni.     

Submodule Structure of Generalized Verma Modules Induced from Generic Gelfand-Zetlin Modules

For complex Lie algebra sl(n, C) we study the submodule structure of generalized Verma modules induced from generic Gelfand-Zetlin modules over some subalgebra of type sl(k, C). We obtain necessary and sufficient conditions for the existence of a submodule generalizing the Bernstein-Gelfand-Gelfand theorem for Verma modules.     

On the existence of a single test module

We revisit two questions concerning the existence of a single test module by comparing them with similar questions (see Theorem 3.3). As a corollary, we identify domains over which strongly flat modules and torsion-free Whitehead modules coincide (see Corollary 3.6). We obtain several analogous results to the main theorem under stronger hypotheses (see section 4). In particular, we settle a long-standing question concerning a characterization of almost perfect domains (see Corollary 4.4). We also look into the case when the character module of K and the Matlis-dual of K are isomorphic (see Theorem 5.2).     

相对于半对偶化模的Gorenstein同调维数与Auslander范畴

设$R$是一个局部noether环. 我们在本文中研究了相对于半对偶化模$C$的Gorenstein投射, 内射与平坦模. 给出了$C$-Gorenstein同调维数与$\hat{R}$的Auslander范畴之间的关系.     

Tensor product of C-injective modules

The purpose of this paper is to calculate all the character tables of Hecke algebras associated with finite Chevalley groups of exceptional type and their maximal parabolic subgroups when they are commutative. In the case when the groups are of classical type, the character values of Hecke algebras are expressed by using the q-Krawtchouk polynomials and the q-Hahn polynomials (See [10] and [15]). On the other hand, the character tables of commutative Hecke algebras associated with exceptional Weyl groups and their maximal parabolic subgroups are given in [12]. In §1, we discuss the structure of Hecke algebras and in §2, we calculate all the character tables of these commutative Hecke algebras associated with finite Chevalley groups of exceptional type. Although some of them are well known, we include them for completeness     

Finitely Cogenerated Distributive Modules are Q-Cocyclic

Abstract

In this paper we consider a generalization of Vámos's proposition which asserts that finitely generated artinian and distributive modules are cyclic. Also, we show its duality as an answer to the problem which is shown by him (See Vámos, [Vámos, P. (1978). Finitely generated artinian and distributive modules are cyclic. Bull. London Math. Soc. 10(3):287–288]).     

使用相关内射性对拟连续模的一个刻划

近二十年，许多环与模工作对拟投射模与拟内射模作了各种推广与研究。连续模与拟连续模就是拟内射模的一种推广，拟连续模要比连续模弱。在[2]，作对连续模与拟连续模做了深入的研究。在这篇章中，利用相关内射性给出了拟连续模的一个刻划。     

On a class of semicommutative modules

Let R be a ring with identity, M a right R-module and S = End _R (M). In this note, we introduce S-semicommutative, S-Baer, S-q.-Baer and S-p.q.-Baer modules. We study the relations between these classes of modules. Also we prove if M is an S-semicommutative module, then M is an S-p.q.-Baer module if and only if M[x] is an S[x]-p.q.-Baer module, M is an S-Baer module if and only if M[x] is an S[x]-Baer module, M is an S-q.-Baer module if and only if M[x] is an S[x]-q.-Baer module.     

拟-Armendariz模

For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm(N)Mm(R) is quasi-Armendariz if and only if Tm(N)Tm(R) is quasi-Armendariz, where Mm(N) and Tm(N) denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if N[x]R[x] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.     

A note on tilting sequences

We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.      

The isomorphism problem for uniserial modules over an arbitrary ring

Abstract

First, we give a partial solution to the isomorphism problem for uniserial modules of finite length with the help of the morphisms between these modules. Later, under suitable assumptions on the lattice of the submodules, we give a method to partially solve the isomorphism problem for uniserial modules over an arbitrary ring. Particular attention is given to the natural class of uniserial modules defined over algebras given by quivers.     

F－V－环的广义内射性刻划

设Ｆ是含单位元的结合环Ｒ上的左Ｇａｂｒｉｅｌ拓朴，称Ｒ是Ｆ－Ｖ－环，如果商范畴（Ｒ，Ｆ）－Ｍｏｄ中的所有单对象都是内射对象。本文我们利用左Ｒ－模的ｖＮ－内射性及拟内射性给出Ｆ－Ｖ－环的特征刻划。     

F－V－环的广义内射性刻划

设Ｆ是含单位元的结合环Ｒ上的左Ｇａｂｒｉｅｌ拓朴，称Ｒ是Ｆ－Ｖ－环，如果商范畴（Ｒ，Ｆ）－Ｍｏｄ中的所有单对象都是内射对象。本文我们利用左Ｒ－模的ｖＮ－内射性及拟内射性给出Ｆ－Ｖ－环的特征刻划。     

Gorenstein代数上的逼近扩张

本文引进了（极小）逼近扩张，证明了极小逼近扩张在Ｇｏｒｅｎｓｔｅｉｎ代数上的存在性和唯一性，并给出了极小逼近扩张的一个应用．     

相关扭曲Hopf模的基本同构定理与相关Yetter-Drinfel'd模

扭曲的方法在构造新的代数结构与余代数结构中起了重要的作用.本文首先把扭曲的方法运用到模与余模的构造中,得到扭曲模和扭曲余模;其次在更加一般的情形下给出相关扭曲Hopf模的基本同构定理;最后考虑在HopfYD模中如何使扭曲模构成相关Yetter-Drinfel'd模和相关Hopf模.     

广义Fitting模的扩张

In this paper, we study the closeness of strongly （∞）-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[X] is strongly hopfian （resp. strongly co-hopfian） in R[X]-Mod, then M is strongly hopfian （resp. strongly co-hopfian） in R-Mod.     

𝔏-Rickart Modules

It is well known that the Rickart property of rings is not a left-right symmetric property. We extend the notion of the left Rickart property of rings to a general module theoretic setting and define 𝔏-Rickart modules. We study this notion for a right R-module M _R where R is any ring and obtain its basic properties. While it is known that the endomorphism ring of a Rickart module is a right Rickart ring, we show that the endomorphism ring of an 𝔏-Rickart module is not a left Rickart ring in general. If M _R is a finitely generated 𝔏-Rickart module, we prove that End _R (M) is a left Rickart ring. We prove that an 𝔏-Rickart module with no set of infinitely many nonzero orthogonal idempotents in its endomorphism ring is a Baer module. 𝔏-Rickart modules are shown to satisfy a certain kind of nonsingularity which we term “endo-nonsingularity.” Among other results, we prove that M is endo-nonsingular and End _R (M) is a left extending ring iff M is a Baer module and End _R (M) is left cononsingular.