【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).更多还原

【Abstract】 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 Jacobson radical of the ring R#S*: J(R#S*)=JS(R)#S* and Jref(R)=(J(R#S*))↓=JS(R).更多还原