关于余极限范畴(英文)

本文研究了余极限范畴.利用余完备Abel范畴的定义,证明了余完备Abel范畴A的余极限范畴Acl是余完备的Abel范畴,并得到一类等价于模范畴的余极限范畴,从而推广了文献[9]中的一些结果.     

A new version of a theorem of Kaplansky

Abstract

A well-known theorem of Kaplansky states that any projective module is a direct sum of countably generated modules. In this paper, we prove the w-version of this theorem, where w is a hereditary torsion theory for modules over a commutative ring.

Communicated by Silvana Bazzoni     

Restricted Kac modules for special contact Lie superalgebras of odd type

We consider the simple restricted modules for special contact Lie superalgebras of odd type over an algebraically closed field of characteristic p>3: We give a suffcient and necessary condition in terms of typical or atypical weights for restricted Kac modules to be simple. In the process, we also determine the socle for each restricted Kac module and the length for each simple restricted module.     

Irreducible representations over the diamond Lie algebra

In this paper, we use Block’s results to classify irreducible modules over the diamond Lie algebra 𝔇. As a corollary, we also give a classification of irreducible modules over the Euclidean algebra 𝔢(2).     

sl(2)的q-变形的不可分解的Harish-Chandra模的分类

本文对sl（2）的q-变形的不可分解的Harish－Chandra模进行了分类．     

Cohomological Properties of the Canonical Globalizations of Harish–Chandra Modules

In this note we draw consequences of theorems of Kashiwara–Schmid, Casselman, and Schneider–Stuhler. Canonical globalizations of Harish–Chandra modules can be considered as coefficient modules for cohomology groups with respect to cocompact discrete subgroups or nilpotent Lie algebras. We obtain finiteness and comparison theorems for these cohomology groups.     

Equivalence Representation for Nonsingular M-matrices

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绝对余纯模

引入了绝对纯模的对偶概念－－绝对余纯模，还入了半遗传环的对偶概念－余半遗传环，给出了绝对余纯模的一些等价刻画，研究了绝对余纯模的一些性质，并用绝对余纯模刻画了余正则环和余半遗传环。     

Degenerations of <Emphasis Type="Italic">k</Emphasis>[<Emphasis Type="Italic">t</Emphasis>]/(<Emphasis Type="Italic">t</Emphasis><Superscript>r</Superscript>)-Modules Giving Stratification of the Orbits

Let Λ be a finitely generated associative k-algebra where k is an algebraically closed field. For each natural number d, we have the variety of d-dimensional module structures on k^d given by the multiplication of the elements from a generating set of Λ. The general linear group Gl_d(k) acts on this variety by conjugation and the orbits under this action correspond to isomorphism classes of d-dimensional Λ-modules. For two d-dimensional Λ-modules M and N one says that M degenerates to N if the orbit corresponding to N is in the Zariski-closure of the orbit corresponding to M. Now in this situation the stabilizers of the elements in the orbit corresponding to N acts on the orbit corresponding to M. In this paper we characterize degenerations of k[t]/(t^r)-modules with the property that for each y in the orbit corresponding to N, there is an x_y in the orbit corresponding to M such that the orbit corresponding to M is the disjoint union of orbits of the x_y’s under the action of the stabilizer of y where y runs through the orbit corresponding to N. Presented by Idun ReitenMathematics Subject Classifications (2000) 14L30, 16G10.