分次环的分次Excellent扩张

本文引进了分次环的分次Excellent扩张概念,设S=⊕_(g∈G)S_g是R=⊕_(g∈G)R_g的分次Excellent扩张,证明了S是分次右V-环当且仅当R是分次右V-环,S是分次PS-环当且仅当R是分次PS-环,S是分次Von Neumann正则环当且仅当R是分次Von Neumann正则环。     

有限群分次环上的余挠对研究

本文研究了余挠对在有限群分次和非分次情况下的联系.利用分次理论以及相对同调,我们首先研究了R是任意环G是有限群的情况下,余挠对在R-模范畴以及斜群环S=R*G-模范畴之间的关系;然后我们研究了R-gr范畴中刚性余挠对的等价刻画,同时给出了余挠对在R-gr范畴与R-模范畴之间的关系,其中R是G分次环,群G是有限群且|G|^-1∈R.     

G-集分次模的分次自同态环

设G是任意群,本文给出了G-集G／H-分次模的分次自同态环的刻画．特别地,对我们证得N（H）／H-分次自同态环END（G／H,R）－gr（M）等于分次环ENDR（M）N（H）／H.     

群分次环的本原性及分次本原性

设A是一个用有限群G分次的环,本文给出了Smash积A＃G~*为本原环的一个判别准则,并证明了群分次环的每一个本原理想必定包含一个分次本原理想。作为一个推论,得到已被Cohen和Montgomery证实的Bergman猜想的另一个证明。此外还得到了A_1为本原环或单环的判别。     

分次可除模

对于G一分次环R，我们证明如下结论：(1）若R是分次正则环，则R上的任一分次左R一模都是分次可除模；(2)若R分次非退化且M是分次可除左R—模，则Me是可除左Re一模；(3)若G是有序群，M是可除左R一模，刚M^～和M～是分次可除左R一模，其中M为分次左R一模N的子模。     

分次Abel正则环的结构

首先给出了 gr-正则环为分次除环的两个充要条件 ,其次讨论了分次正则环r G(R)和分次 Jacobson根 JG(R)之间的关系 ,最后给出了分次 Abel正则环的结构定理 .     

分次FS—环

本文引进群分次环上分次模的分次ＦＳ－模的概念,利用分次极大分次左理想给出分次ＦＳ－环的几个刻画,得到了环Ｒ和群环ＲＧ,分次环Ｒ和分次环的群环Ｒ「Ｇ」间的几个等价条件。     

G-分次环与G-集的冲积(Smash Product)

对任意群G,[1]中研究了G-分次环与可迁有限G-集的冲积.在本文中我们对任意可迁G-集A,讨论了G-分次环R与G-集A的冲积,从而推广了[2][3]中给出的关于G-分次环与群G的冲积的主要结果.     

G-分次环与G-集的冲积(Smash Product)

对任意群G,[1]中研究了G-分次环与可迁有限G-集的冲积.在本文中我们对任意可迁G-集A,讨论了G-分次环R与G-集A的冲积,从而推广了[2][3]中给出的关于G-分次环与群G的冲积的主要结果.     

强分次环与非分次模范畴

设R是强群G-分次环,日是G的指数有限的子群.本文讨论强分次环R上一般非分次模的一些性质.首先证明一个与非分次R-模和R(H)-子模有关的Maschke-type定理,然后证明从模范畴R(H)-mod到R-mod的函子HomR(H)(R,-)与R(?)R(H)-是一对自然同构的函子以及等价条件.     

分次根与自反根

Ｍ．Ｂｅａｔｔｉｅ和Ｐ．Ｓｔｅｗａｒｔ在文（１）中讨论了六种分次根与相应自反根的关系。作为该文的继续，本文首先定义了Ｋｏｅｔｈｅ根并讨论它与Ｋｏｅｔｈｅ自反根的关系。其次，进一步给出Ｌｅｖｉｔｚｋｉ自反根的刻画。最后，我们指出文（１）的两个错误结论，证明分次ｖｏｎ Ｎｅｕｍａｎｎ根与ｖｏｎ Ｎｅｕｍａｎ自反根恰好相等。     

分次FS-环(英)

本文引进群分次环上分次模的分次FS－模的概念,利用分次极大分次左理想给出分次FS－环的几个刻画,得到了环R和群环RG,分次环R和分次环的群环R[G]间的几个等价条件．     

Groups with Polycyclic Non-Normal Subgroups

The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property X. Groups whose non-normal subgroups satisfy certain finite rank conditions are studied in this article. In particular, a classification of groups in which every subgroup is either normal or polycyclic is given.(Dedicated to Mario Curzio on the occasion of his 70th birthday)1991 Mathematics Subject Classification: 20F16     

有足够幂等元的群分次环上的Morita对偶

首先定义了具有足够幂等元的群分次环的Ｓｍ ａｓｈ 积并讨论其性质,其次,借助Ｓｍ ａｓｈ 积给出了这类分环上的分次Ｍｏｒｉｔａ对偶的刻划．     

On a Problem of P. Hall about Groups Isomorphic to all their Non-Trivial Normal Subgroups

A scheme of construction of infinite groups, other than simplegroups, free groups of infinite rank and the infinite cyclicgroup, which are isomorphic to all their non-trivial normalsubgroups is presented. Some results about the automorphismgroups of simple infinite groups are also obtained. In particular,it is proved that there is an infinite group G of any sufficientlylarge prime exponent p (or which is torsion-free) all of whoseproper subgroups are cyclic, and such that the groups Aut Gand Out G are isomorphic. The proofs use the technique of gradeddiagrams developed by A. Yu. Ol'shanskii. 1991 Mathematics SubjectClassification: 20F05, 20F06.     

Symmetric complete intersections

We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these ideals and describe formulas for the graded characters of the corresponding quotient rings.     

Z_n分次代数的Hochschild上同调群

本文给出了Z_n分次代数A的Hochschild上同调群的定义,对低阶Hochschild上同调群进行了刻画.利用第一阶Hochschild上同调群给出了Z_n分次代数为分次可分代数的充要条件,证明了第二阶Hochschild上同调群的零次分支与A的Hochschild扩张之间的一一对应关系.     

Graded automorphism group of TKK algebra

The classification of extended affine Lie algebras of type A_1 depends on the Tits-Kantor- Koecher (TKK) algebras constructed from semilattices of Euclidean spaces.One can define a unitary Jordan algebra J(S) from a semilattice S of R~v (v≥1),and then construct an extended affine Lie algebra of type A_1 from the TKK algebra T(J(S)) which is obtained from the Jordan algebra J(S) by the so-called Tits-Kantor-Koecher construction.In R~2 there are only two non-similar semilattices S and S′,where S is a lattice and S′is a non-lattice semilattice.In this paper we study the Z~2-graded automorphisms of the TKK algebra T(J(S)).     

Flat and Stably Flat Modules

We study Kropholler's generalisation of Lazard's criterion for a module to be flat. The context is complete cohomology and modules of type (FP)_∞. Let G be a group in the class ₁ of groups which act on a finite dimensional contractible cell complex with finite stabilisers and let R be a strongly G-graded algebra. We provide a characterisation of the stably flat R-modules under the assumption that R₁ is coherent of finite global dimension.