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