共查询到20条相似文献,搜索用时 0 毫秒
1.
We introduce the graded version of the antisimple primitive radical $ {\user1{\mathcal{S}\mathcal{J}}} $ , the graded antisimple primitive radical $ {\user1{\mathcal{S}\mathcal{J}}}_{G} $ . We show that $ {\user1{\mathcal{S}\mathcal{J}}}_{G} = {\user1{\mathcal{S}\mathcal{J}}}_{{{\text{ref}}}} = {\user1{\mathcal{S}\mathcal{J}}}^{G} $ when |G| < ∞, where $ {\user1{\mathcal{S}\mathcal{J}}}_{{{\text{ref}}}} $ denotes the reflected antisimple primitive radical and $ {\user1{\mathcal{S}\mathcal{J}}}^{G} $ denotes the restricted antisimple primitive radical. Furthermore, we discuss the graded supplementing radical of $ {\user1{\mathcal{S}\mathcal{J}}}^{G} $ . 相似文献
2.
3.
分次根、弱分次根与自反根 总被引:12,自引:0,他引:12
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. 相似文献
4.
5.
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). 相似文献
6.
JacobsonRadicalsGradedbyG-setsSunJianhua(孙建华)(DepartmentofMathematics,Teacher'sCollege,YangzhouUniversity,Yangzhou,Jiangsu,22... 相似文献
7.
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. 相似文献
8.
9.
10.
本文证明了对有限群分次环R而言,下列条件等价:(1)R是左gr-自内射环(左gr-PF环,左gr-QF环,左gr-线性紧环).(2)R是左自内射环(左PF环,左QF环,左线性紧环).(3)R#G*是左自内射环(左PF环,左QF环,左线性紧环). 相似文献
11.
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。 相似文献
12.
分次环的分次Jacobson根 总被引:25,自引:2,他引:25
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. 相似文献
13.
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. 相似文献
14.
A. L. Kanunnikov 《Journal of Mathematical Sciences》2014,197(4):525-547
For an associative gr-semiprime ring R with identity graded by a group, the orthogonal graded completion O gr(R) is constructed. A criterion for the orthogonal completeness of the maximal right graded quotient ring Q gr(R) is proved. The ring Q gr(R) need not be orthogonally complete, as opposed to the ungraded case. 相似文献
15.
群分次环的本原性及分次本原性 总被引:1,自引:0,他引:1
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。 相似文献
16.
17.
18.
V. E. Govorov 《Mathematical Notes》1972,12(2):552-556
We study the growth in the number of dimensions dn of the homogeneous component of a graded algebra with a finite number of defining relations and generators for the Poincaré series dnxn. It is proved that if the defining relations are words, the Poincaré series is a rational function. In the general case inequalities are proved linking the number of dimensions dn with the number of generators defining relations and their degree.Translated from Matematicheskie Zametki, Vol. 12, No. 2, pp. 197–204, August, 1972. 相似文献
19.
20.
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. 相似文献