| 半群分次环上的Morita对偶 |
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| 引用本文： | 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. DOI: 10.3770/j.issn.1000-341X.2008.02.006 |
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| 作者姓名： | 张子龙 侯波 李艳梅 |
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| 作者单位： | 河北师范大学数学与信息科学学院, 河北 石家庄 050016;河北师范大学数学与信息科学学院, 河北 石家庄 050016;北京市7227信箱, 北京 100072 |
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| 基金项目： | 国家自然科学基金 , 河北省自然科学基金 , 河北省教育厅科研项目 |
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| 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.
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| 关 键 词： | semigroup bigraded R-A-bimodule Q-reflected semigroup graded Morita duality. 半群分次环 Morita duality 对偶 Rings Semigroup closed semigroup balanced result equivalence graded module category paper studies rings |
| 收稿时间： | 2005-10-10 |
| 修稿时间： | 2005-10-10 |
Morita Duality of Semigroup Graded Rings |
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| ZHANG Zi Long,HOU Bo and LI Yan Mei. Morita Duality of Semigroup Graded Rings[J]. Journal of Mathematical Research with Applications, 2008, 28(2): 279-286. DOI: 10.3770/j.issn.1000-341X.2008.02.006 |
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| Authors: | ZHANG Zi Long HOU Bo LI Yan Mei |
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| Affiliation: | 1. College of Mathematics and Information Science,Hebei Normal University,Hebei 050016,China
2. 7227 Mail Box,Beijing 100072,China |
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| Abstract: | This paper studies Morita duality of semigroup-graded rings,and discusses an equivalence between duality functors of graded module category and bigraded himodules.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 Ref(RQ),Ref(QA) is closed under graded submodules and graded quotients. |
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| Keywords: | semigroup bigraded $R$-$A$-bimodule $Q$-reflected semigroup graded Morita duality. |
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