Direct summands of modules which satisfy (C-11)

Smith P., Tercan A.

ALGEBRA COLLOQUIUM, vol.11, no.2, pp.231-237, 2004 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2004
  • Journal Name: ALGEBRA COLLOQUIUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.231-237
  • Hacettepe University Affiliated: No

Abstract

A module M satisfies (C-11) if every submodule of M has a complement which is a direct summand of M. It is shown that there exists a commutative domain R and an R-module M which satisfies (C-11) and has a direct summand K that does not satisfy (C-11). In contrast, if a module M satisfies (C-11) axnd r(M) is a direct summand of M for a left exact preradical r, then r(M) satisfies (C(11)i).