Meta-sided exchange环及其扩张

Meta-sided Exchange Rings and Their Extensions

讨论了meta-sided exchange环的性质。证明了如果R是Abelian meta-sided exchange环,则对R的任意素理想P,都有R/P是局部环;如果R是Abelian环,(S,≤)是严格序幺半群且对任意s∈S,都有0≤s,则广义幂级数环[[RS,≤]]是meta-sided exchange环当且仅当R是meta-si-ded exchange环。

Some properties of meta-sided exchange rings are discussed in this paper.It is shown that if R be a meta-sided exchange ring with all idempotents central,.R/P is local ring for any prime ideal PofR.And it also proved that let R be an Abelian ring and（S,≤） a strictly ordered monoid satisfying the condition that 0≤s for every s∈S,then generalized power series ring ] is meta-sided exchange ring only if R is meta-sided exchange ring.