广义半$\pi$-正则环

Generalized Semi-$\pi$-Regular Rings

中文关键词:  $GP$-内射环  半$\pi$-正则环  广义半正则环  广义半$\pi$-正则环.

英文关键词:$GP$-injective rings  semi-$\pi$-regular rings  generalized semiregular rings  generalized semi-$\pi$-regular rings.

中文摘要:

      本文给出了广义半$\pi$-正则环的定义,证明了广义半$\pi$-正则环是半$\pi$-正则环和$GP$-内射环的非平凡推广,并且讨论了广义半$\pi$-正则环的一些性质,将广义半正则环和$GP$-内射环的部分结论进行了推广.

英文摘要:

      In this paper, the concept of right generalized semi-$\pi$-regular rings is defined. We prove that these rings are non-trival generalizations of both right $GP$-injective rings and semi-$\pi$-regular rings. Some properties of these rings are studied and some results about generalized semiregular rings and $GP$-injective rings are extended.