ON THE STRUCTURE OF PRIMITIVE RINGS

In this paper the author introduces two concepts, i. e. the concept of so-colled v-socles of primitive rings and the concept of a pair of dual modules. Then the author establishes a general structure theorem for primitive rings with v-socles, which implies the well-known structure theorem for primitive rings with usual non-zero socles.     

拓扑分次C*-代数中的对角不变理想

We study diagonal invariant ideals of topologically graded C＊-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author＇s previous works on this topic.     

On Minimal Graded One-sided Ideals and Graded Primitive Rings

In this paper, sturcture theorems are given for graded primitive rings with minimal graded one-sided ideals and arbitrary minimal graded one-sided ideals of general group-graded rings respectively.     

CYCLIC CODES OVER FORMAL POWER SERIES RINGS

In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained.     

Generalized Green Correspondence of Graded Modules

The author studies the Green correspondence and quasi-Green correspondence for indecomposable modules over strongly graded rings. The motivation is to investigate the influence of induction and restriction processes on indecomposability of graded modules.     

偏倾斜模和倾斜模的分次与非分次性质

This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded partial tilting modules, there exist the Bongartz complements in the category of graded A-modules.     

Group-Craded Regular R-Modules and R#G^-Modules

For any group G and G-graded ring R with identity,We discuss the relations between graded Von Neumann regularity of graded R↑_-modules and von Neumann regularity of R-modus,Re-moduls and unital R#G^*;modules.Then we obtain some results about graded rings.We also prove Maschke-type theorem,generalizing[1,Theorem2.3].     

分次单环的结构

A characterization of gr-simple rings is given by using the notion of componentwise-dense subrings of a full matrix ring over a division ring. As a consequence, any G-graded full matrix ring over a division ring is isomorphic to a dense subring of a full matrix ring with a good G-grading. Some conditions for a grading of a full matrix ring to be isomorphic to a good one are given, which generalize some results in: Dascascu, S., Lon, B., Nastasescu, C. and Montes, J. R., Group gradings on full matrix rings, J. Algebra, 220(1999), 709-728.     

A Note on Rings and Modules Graded by Some Special Groups

In this note we prove that the prime madicals of some graded rings and the scoles of some graded modules are also graded. The results on the relations between the prime radical and the graded prime radical are also presented. Moreover, the relations between a graded ring and its initial subring are studied.     

关于多项式函数的计数

Polynomial functions （in particular, permutation polynomials） play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutative rings is discussed. Let A be a general finite commutative local ring. Under a certain condition, the counting formula of the number of polynomial functions over A is obtained. Before this paper, some results over special finite commutative rings were obtained by many authors.     

分次P-根

在一般Monoid分次环范畴中定义了一种新的分次根——分次P-根,得到分次环的一个结构定理,证明分次P-根是一个分次特殊根,给出了它的分次模刻划,讨论了它与自反P-根的关系。     

群分次环的分次Levitzki根

建立了分次环的分次Levitzki根,并给出了分次Levitzki半单环的结构定理及相关结果.     

分次环的分次Jacobson根

本文通过引入弱拟正则元的概念，对一般Ｍｏｎｏｉｄ分次环Ａ（未必有１）给出以内部元素刻划的分次Ｊａｃｏｂｓｏｎ根ＪＧ（Ａ）．证明当Ａ有１时，ＪＧ（Ａ）与通常定义的Ｊｇ（Ａ）相等．对ＪＧ（Ａ）性质的讨论，推广了最近的许多结果．作为应用，我们给出了Ａｒｔｉｎ分次环的全部基本结构定理．     

分次环的分次根

给出了建立分次环根的一般方法．作为其应用，建立了分次环的分次Brown—McCoy根，并给出了Brown—McCoy半单分次环的结构定理．     

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。     

分次直投射模及应用

本文引进分次直投射模的概念,得到分次直投射模的一个判定定理,并利用分次直投射模刻划了分次左遗传环,分次左半遗传环,分次左半单环和分次左PP-环,     

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。     

Gr-凝聚环的分次FP-内射维数

引进了分次FP-内射维数，对Gr-凝聚环的分次FP-内射维数作了刻划，将Stentrom等人的若干工作推广到分次环上．     

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。