交换半群环的分式环  

COMMUTATIVE SEMIGROUP RING OF FRACTIONS

作　　者：王德胜[1] 李师正[1] 张玉芬[1] 

机构地区：[1]山东师范大学,济南250014

出　　处：《纯粹数学与应用数学》1996年第1期85-87,共3页Pure and Applied Mathematics

摘　　要：设含幺交换环及对其乘法子集T的分式环为R_T,交换幺半群S在其子半群∑处局部化为S∑,则A={tu|t(?)T,u(?)∑}是半群环R[S]的乘法子集。本文证明了R[S]对于A的分式环R[S]_A同构于半群环R_T[S_∑]。Let RT be a ring of fractions of a commutative ring R with respect to its multiplicatively closed subset T, and Let S ∑be the localization of a monoid S over its submonoid ∑. Let A= {tu|t ∈ T,u ∈ ∑}, then A is a multiplicatively closed subset of the commutative semigroup ring R[S]. We prove in this paper that the ring of fractions of R[S] with respect to A is isomorphic to the commutative semigroup ring RT[S∑].

关 键 词：分式环 半群环 交换半群环 交换幺半群 

分 类 号：O153.3[理学—数学]