张子龙,侯波,李艳梅.半群分次环上的Morita对偶[J].数学研究及应用,2008,28(2):279~286 |
半群分次环上的Morita对偶 |
Morita Duality of Semigroup Graded Rings |
投稿时间:2005-10-10 修订日期:2007-07-13 |
DOI:10.3770/j.issn:1000-341X.2008.02.006 |
中文关键词: 双分次$R$-$A$双模 $Q$自反的 半群分次Morita对偶. |
英文关键词:semigroup bigraded $R$-$A$-bimodule $Q$-reflected semigroup graded Morita duality. |
基金项目:国家自然科学基金(No.10571043;10671053); 河北省自然科学基金(No.102132); 河北省教育厅科学基金(No.2004108). |
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中文摘要: |
本文主要研究了半群分次环上的Morita对偶问题,讨论了半群分次模范畴上满足某种条件的对偶函子与双分次双模之间的等价关系.得到重要定理:半群双分次$R$-$A$双模$Q$定义一个半群分次Morita对偶当且仅当${}_RQ_A$是分次忠实平衡的,且${\rm Ref}({}_RQ)$, ${\rm Ref}(Q_A)$对分次子模和分次商模是封闭的. |
英文摘要: |
This paper studies Morita duality of semigroup-graded rings, and discusses an equivalence between duality functors of graded module category and bigraded bimodules. An important result is obtained: A semigroup bigraded $R$-$A$-bimodule $Q$ defines a semigroup graded Morita duality if and only if $Q$ is gr-faithfully balanced and ${\rm Ref}({}_RQ)$, ${\rm Ref}(Q_A)$ is closed under graded submodules and graded quotients. |
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