幂级数π-Armendariz环

Power series π-Armendariz rings

引入幂级数π-Armendariz环的概念,研究了幂级数π-Armendariz环的扩张,证明了如果环R是具有幂零有界指数的NI环,且为α-容许环,则R[x;α]是幂级数π-Armendariz环.同时讨论了幂级数环的幂零p.p.性和弱zip性.

The concept of a power series π- Armendariz ring is proposed. The extensions of π- Armendariz rings are studied which shows that if R is of bounded index,an NI ring and a-compatible, then R[x;a] is π-Armendariz. Meanwhile, the nilpotent p. p. property and weak zip property of a power series ring are given.