关于素中心的正则环(英文)

On Regular Rings with Prime Centers

如果R是具有素中心的环 ,则R是SF -环 ,当且仅当R是正则环 ,也当且仅当R是强正则环。这成立的充要条件是对每个平坦左R -模M及 φ∈EndRM ,Soc(M/Imφ)是平坦的。我们同时证明了若正则环R具有素中心 ,则所有单左 (右 )R -模是内射的。

In this paper we show that if R is a ring having a prime center then R is SF-ring if and only if R is a regular ring and also if and only if R is a strongly regular rings, which is supported if and only if (M/Imφ) is flat for each flat left R-module M and each φ∈End RM.We also show that if R is a regular ring having a prime center then all simple left (right) R-modules are injective.