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局部单位元半群分次环

The Rings Graded by Locally Identities Semi-groups
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摘要 设S为有限局部单位元半群,R为S—分次环.首先定义了S—分次环R在半群S上的冲积R#S*,证明了模范畴R#S*-M od与分次模范畴(S,R)-g r之间的等价性,并进一步研究了局部单位元半群分次环的分次Jacobson根及其相关的自反根的关系,得到重要关系式J(R#S*)=JS(R)#S*及Jref(R)=(J(R#S*))↓=JS(R). Let S be a locally identities semigroup, R a locally unital S-graded ring. In this paper, we define the notion of the smash product R #S ^* and study the equivalence between the category R#S^*- Mod and the graded (S,R)-gr. Moreover, we discuss the propoties of the related radicals and obtain the relations on the Jaeobson radical of the ring R#S^* : J(R#S^* ) = Js(R)#S^* and Jref(R) = (J(R#S^*))↓ = Js(R).
出处 《数学的实践与认识》 CSCD 北大核心 2009年第22期111-117,共7页 Mathematics in Practice and Theory
基金 国家自然科学基金(10571043 10671053) 河北省自然科学基金(A2008000135 A2009000253) 河北师范大学博士基金(L2006B06)
关键词 冲积 局部单位元半群 局部单位分次环 smash product locally identiries semigroup locally unital graded ring
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参考文献10

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