| 分次Morita Contexts与分次根 |
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| 引用本文： | 王尧,任艳丽. 分次Morita Contexts与分次根[J]. 数学学报, 2006, 49(6): 1367-137. DOI: cnki:ISSN:0583-1431.0.2006-06-025 |
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| 作者姓名： | 王尧 任艳丽 |
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| 作者单位： | 南京晓庄学院数学系,南京210017 |
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| 基金项目： | 国家自然科学基金资助项目（10271017） |
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| 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)．
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| 关 键 词： | 分次Morita Context 分次素根 分次Jacobson根 分次Koethe根 |
| 文章编号： | 0583-1431（2006）06-1367-06 |
| 收稿时间： | 2005-06-26 |
| 修稿时间： | 2005-06-262005-09-30 |
Graded Morita Contexts and Graded Radicals |
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| Yao WANG,Yan Li REN. Graded Morita Contexts and Graded Radicals[J]. Acta Mathematica Sinica, 2006, 49(6): 1367-137. DOI: cnki:ISSN:0583-1431.0.2006-06-025 |
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| Authors: | Yao WANG Yan Li REN |
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| Affiliation: | Department of Mathematics, Nanjing Xiaozhuang University, Nanjing 210017, P. R. China |
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| Abstract: | LetM={A=■_(g∈G)A_g,V=■_(g∈G)V_g,W=■_(g∈G)W_g,B=■_(g∈G)B_g} and(,),[,]be a G-graded Morita Context with(V,W)=A and[W,V]=B,where A and B are graded ring with 1.We show that r_G(B)=[W,r_G(A)V]=[Wr_G(A),V],r_G(A)=(V,r_G(B)W)=(Vr_G(B),W), where r_G 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. |
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| Keywords: | graded Morita Context graded prime radical graded Jacobson radical graded Koethe radical |
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