分次根、弱分次根与自反根

本文在一般群分次环范畴中,给出了典型分次根NG,LG,gG,rG和KG的元素刻划.通过建立弱分次根概念,研究了自反根Nref,Lref,gref,rref和Kref的性质,探讨了这些分次根和与它们相对应的自反根的关系．     

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。     

分次广义Γ-环的Brown-McCoy根

研究了分次广义Γ-环的弱强分次B row n-M cC oy根与拟弱强分次B row n-M cC oy根,并从不同角度刻划了分次广义Γ-环的弱强分次B row n-M cC oy根.证明了任何一个分次广义Γ-环都有弱强分次B row n-M cC oy根和拟弱强分次B row n-M cC oy根,而且弱强分次B row n-M cC oy根小于等于拟弱强分次B row n-M c-C oy根.     

分次环的有限正规扩张

本文研究了群分次环的有限正规分次扩张问题．利用经典环论方法，得到一个群分次环与其有限正规分次扩张环之间关于分次Jacobson根和分次素根的关系，同时，给出了分次情形的Cutting down定理和Lying over定理．     

分次环的分次σ-根

在分次环类中定义H-关系,利用H-关系给出分次σ-根的定义,并进一步得到分次环类γ是分次σ-根的几个充分必要条件.     

弱分次周期根

对一般群分次环境立了弱分次周期根的概念,证明它是一个分次特殊根,给出了它的分次模刻,讲座了它与自反周期根的关系。     

分次Morita Contexts与分次根

设M={A=⊕_(g∈G)A_g,V=⊕_(g∈G)V_g,W=⊕_(g∈G)W_g,B=⊕_(g∈G)B_g}与(,),[,]是一个G-分次Morita Context,且满足(V,W)=A,[W,V]=B,A,B都有单位元．本文证明τG(B)：[W,ΥG(A)V]=【WΥc(A),V],ΥG(A)=(V,ΥG(B)W)=(VΥG(B),W)其中ΥG代表P_G(分次素根),J_G(分次Jacobson根),K_G(分次Koethe根),L_G(分次Levitzki根)和s_G(分次强素根),us_G(分次一致强素根)．     

分次环的分次根(英文)

本文建立了分次环的分次Baer根及分次Koethe根.利用根的结构定理,给出了相应半单分次环的结构定理.     

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．     

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。     

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.     

环的根性质

研究的对象是不含单位元分次环 R,首先证明了有关 Jacobson根的重要性质 J( R) =J( S)∩ R,其中 S =R× Z.然后利用它得到了一些好的性质     

关于挠自由群分次环的注记

本文推广ＣＮａｓｔａｓｅｃｕ，Ｆ．ＶａｎＯｙｓｔａｅｙｅｎ的有关结果，并在一定条件下回答了Ｋ．Ｒ．Ｆｕｌｌｅｒ等人的公开问题．     

Separable Groupoid Rings

We show that groupoid rings are separable over their ring of coefficients if and only if the groupoid is finite and the orders of the associated principal groups are invertible in the ring of coefficients. We use this to show that if we are given a finite groupoid, then the associated groupoid ring is semisimple (or hereditary) if and only if the ring of coefficients is semisimple (or hereditary) and the orders of the principal groups are invertible in the ring of coefficients. To this end, we extend parts of the theory of graded rings and modules from the group graded case to the category graded, and, hence, groupoid graded situation. In particular, we show that strongly groupoid graded rings are separable over their principal components if and only if the image of the trace map contains the identity.     

具有非零分次基座的分次本原环的刻划

In this paper, we characterize the structure of group graded primitive rings having minimal graded one-sided ideals in terms of graded dual modules. We also show that two structure representations of this class of graded primitive rings are both in a sense uniquely determined by the graded primitive rings considered.     

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．     

Lattices of Radicals of Involution Rings

A lattice-theoretic approach to the radical theory of rings was initiated by Snider. In the current paper, we extend this approach to the radical theory of involution rings. We show that the classes of hereditary radicals, radicals satisfying ADS and invariant radicals form complete sublattices of the lattice of all radicals of involution rings. We show that certain sublattices are isomorphic to sublattices of the lattice of radicals of rings. We characterize the atoms of certain lattices of radicals of involution rings.1991 Mathematics Subject Classification: 16W10, 16N99, 06B99     

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．     

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.