亚直不可约广义DQC—环

Subdirectly Irreducible Generalized-DQC Rings

本文定义了广义DQC一环,给出忠实与不忠实的广义DQC一环为亚直不可约的刻划,推广了W.Burgcss等人在DQC一环上的相应的工作.

A ring R is defined as a generalized -DQC ring if cach nonzero ideal I of R is definitely IQ0, Where Q is the quasi-centre of R. We have a main result: Let R a faithful generalized-DQC ring, then R is subdirctly irredncible iff there exists jQ\{0} such that (l)RD is a simple ring with l where D=r (jR); (2)jaD, aQ{rR |rR D ana aRjR}。