ON (SEMI)REGULAR MORPHISMS


Truong Cong Quynh T. C. Q. , Kosan M. T. , Le Van Thuyet L. V. T.

COMMUNICATIONS IN ALGEBRA, vol.41, no.8, pp.2933-2947, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 8
  • Publication Date: 2013
  • Doi Number: 10.1080/00927872.2012.667855
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2933-2947
  • Gazi University Affiliated: No

Abstract

Let M and N be right R-modules. Hom(M, N) is called regular if for each fHom(M, N), there exists gHom(N, M) such that f=fgf. Let [M, N]=Hom(R)(M, N). We prove that if M is finitely generated, then [M, N] is regular if and only if every homomorphism MN is locally split. In this article, we also study the substructures of Hom(M, N) such as the Jacobson radical J[M, N], the singular ideal [M, N], and the co-singular ideal delta[M, N]. We prove several new results. The question is to characterize when the Jacobson radical is equal to the singular ideal [M, N] or the co-singular ideal delta[M, N] under injectivity and projectivity.