A ring R with unity is called semiclean, if each of its elements is the sum of a unit and a periodic. Every clean ring is semiclean. It is not easy to characterize a semiclean group ring in general. Our purpose is to ...A ring R with unity is called semiclean, if each of its elements is the sum of a unit and a periodic. Every clean ring is semiclean. It is not easy to characterize a semiclean group ring in general. Our purpose is to consider the following question： If G is a locally finite group or a cyclic group of order 3, then when is RG semiclean？ Some known results on clean group rings are generalized.展开更多
进一步将二阶Morita Context环上的部分性质推广到了三阶Morita Context环上.设O=[R C E A S F B D T]是三阶Morita Context环,证明了:1)O是π-正则的(或半Clean的、Exchange的、Potent的、GM-环)当且仅当R、S和T也是该类环;2)O是左Morp...进一步将二阶Morita Context环上的部分性质推广到了三阶Morita Context环上.设O=[R C E A S F B D T]是三阶Morita Context环,证明了:1)O是π-正则的(或半Clean的、Exchange的、Potent的、GM-环)当且仅当R、S和T也是该类环;2)O是左Morphic环当且仅当R、S、T是左Morphic的,且A=B=C=D=E=F=0.展开更多
设(A,B,V,W,ψ,φ)是一个Morita Context,具有一对零态射ψ=0,φ=0,C= (A V W B)是对应的Morita Context环.本文给出了C与A,B,V,W之间关于环的π-正则性、semiclean性、Mophic性和环的Exchgange性、Potent性、GM性的关系.
基金Supported by the National Natural Science Foundation of China(Grant No.11401009)the Natural Science Foundation of Ahui Province(Grant No.1408085QA01)
文摘A ring R with unity is called semiclean, if each of its elements is the sum of a unit and a periodic. Every clean ring is semiclean. It is not easy to characterize a semiclean group ring in general. Our purpose is to consider the following question： If G is a locally finite group or a cyclic group of order 3, then when is RG semiclean？ Some known results on clean group rings are generalized.
文摘进一步将二阶Morita Context环上的部分性质推广到了三阶Morita Context环上.设O=[R C E A S F B D T]是三阶Morita Context环,证明了:1)O是π-正则的(或半Clean的、Exchange的、Potent的、GM-环)当且仅当R、S和T也是该类环;2)O是左Morphic环当且仅当R、S、T是左Morphic的,且A=B=C=D=E=F=0.
文摘设(A,B,V,W,ψ,φ)是一个Morita Context,具有一对零态射ψ=0,φ=0,C= (A V W B)是对应的Morita Context环.本文给出了C与A,B,V,W之间关于环的π-正则性、semiclean性、Mophic性和环的Exchgange性、Potent性、GM性的关系.
