Semiclean环及其扩张  

Semiclean rings and their extensions

作　　者：郭莉琴[1] 汪国军[2] 

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001 [2]浙江大学数学系,浙江杭州310027

出　　处：《浙江大学学报（理学版）》2012年第1期4-8,共5页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(10871170);浙江省自然科学基金重大项目(D7080064)

摘　　要：对clean环进行了推广,研究了semiclean环,讨论了semiclean环的几个重要性质;证明了(1)R是semi-clean环;(2)R上的形式幂级数环R[[x]]是semiclean环;(3)R上的斜幂级数环R[[x;α]]是semiclean环等价;最后证明了,如果R是环,(S,≤)是严格偏序幺半群且对任意s∈S,都有0≤s,则[[RS,≤]]是semiclean环当且仅当R是semiclean环.Clean rings are generalized and semiclean rings are investigated.Some properties of semiclean rings are discussed.It shows that the followings are equivalent :(1)R is a semiclean ring;(2)Its formal power series ring R is a semiclean ring;(3)Its skew power series ring R is a semiclean ring.Finally,the following result is proved: Let R be a ring and(S,≤) is a strictly ordered monoid satisfying the condition that 0≤s for every s∈S.Then ]is a semiclean ring if and only if R is a semiclean ring.

关 键 词：CLEAN环 semiclean环 形式幂级数环 斜幂级数环 广义幂级数环 

分 类 号：O153.3[理学—数学]