| Morita Duality of Semigroup Graded Rings |
| Received:October 10, 2005 Revised:July 13, 2007 |
| Key Words:
semigroup bigraded $R$-$A$-bimodule $Q$-reflected semigroup graded Morita duality.
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| Fund Project:the National Natural Science Foundation of China (No.10571043; 10671053); the Natural Science Foundation of Hebei Province (No.102132) and the Fundation of the Education Department of Hebei Province (No.2004108). |
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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 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.02.006 |
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