单边exchange环及其扩张

One-sided exchange rings and their extensions

对exchange环进行了推广,研究了单边exchange环。主要讨论了形式幂级数环,斜幂级数环和广义幂级数环的单边exchange性质。证明了在Abelian条件下,exchange环、单边exchange环、clean环是等价的。

Exchange rings are generalized,and one-sided exchange rings are investigated.Some properties of one-sided exchange rings about formal power series ring,skew power series ring and generalized power series ring are discussed.Some equivalent characterizations of one-sided exchange rings are given under the condition of the Abelian ring.