EIFP环

EIFP rings

给出EIFP环的定义,研究EIFP环的一些性质.主要证明了如下结果:①设R为EIFP环,则对每个e∈E(R),有eR(1-e)■J(R);②设R为quasi-normal环,e∈E(R),则R是EIFP环当且仅当eRe及(1-e)R(1-e)都是EIFP环;③R是Abel环当且仅当R是EIFP环和强左幂等自反环;④R是强正则环当且仅当R是von Neumann正则环和EIFP环;⑤R是约化环当且仅当R是n-正则环和EIFP环;⑥EIFP的exchange环有稳定域1.

In this paper, the author introduces the notion of EIFP rings and studies some properties of EIFP rings. The following results are obtained：① Let R be a EIFP ring and eEE（R）. Then eR（1-e） J（R） ; ② Let R be a quasi-normal ring and e∈E（R）. Then R is a EIFP ring if and only if ere and （1-e）R（1-e） are all EIFP rings; ③ R is an Abelian ring if and only if R is a EIFP ring and strongly left idempotent reflexive ring; ④ R is a strongly regular ring if and only if R is a yon Neumann regular ring and EIFP ring; ⑤ R is a reduced ring if and only if R is a n-regular ring and EIFP ring; ⑥ EIFP exchange rings have stable range 1.