分次Morita Contexts与分次根  

Graded Morita Contexts and Graded Radicals

作　　者：王尧[1] 任艳丽[1] 

机构地区：[1]南京晓庄学院数学系,南京210017

出　　处：《数学学报（中文版）》2006年第6期1367-1372,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(10271017)

摘　　要：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)．Abstract LetM={A=＋g∈G Ag1 V=＋g∈G Vg,W=＋9∈G Wg,B=＋g∈GBg}and （,）, [, ] be a G-graded 1Viorita Context with （V, W） = A and [W, V] = B, where A and B are graded ring with 1. We show that rG（B）=[W,rG（A）V]=[WrG（A）,V],rG（A）=（V,rG（B）W）=（VrG（B）,W）,where rc is one of the following graded radicals： the graded prime radical; the graded Jacobson radical; the graded Koethe radical; the graded Levitzki radical; the graded strongly prime radical; the graded uniformly strongly prime radical.

关 键 词：分次Morita CONTEXT 分次素根 分次JACOBSON根 分次Koethe根 

分 类 号：O153.3[理学—数学]