Nonsingular CS-rings coincide with tight PP rings

[摘要] It is shown that if M is a self-generator right R-module, then M is non-M-singular and CS iff M is M-tight and End(M(R)) is a right PP ring. In particular, right nonsingular right CS-rings R are precisely right PP and right R-tight. As applications we show, among others, that for any domain R, R(R)(2) is right CS if and only if R is two-sided Ore domain and two-sided 2-hereditary, giving answer R to an open question known previously in special cases. As another application, we show that for a von Neumann regular ring R, the matrix ring M(n) (R), n > 1, is right weakly selfinjective if and only if R is right selfinjective. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-15

[关键词] CS-rings;weakly selfinjective rings;PP rings;tight rings;n-hereditary rings