When is the SIP (SSP) property inherited by free modules

Birkenmeier G. F., Karabacak F., Tercan A.

ACTA MATHEMATICA HUNGARICA, vol.112, no.1-2, pp.103-106, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 112 Issue: 1-2
  • Publication Date: 2006
  • Doi Number: 10.1007/s10474-006-0067-z
  • Journal Name: ACTA MATHEMATICA HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.103-106
  • Keywords: summand intersection property, summand sum property, C-11-module, SUMMAND INTERSECTION PROPERTY
  • Anadolu University Affiliated: No

Abstract

A right R-module M has right SIP (SSP) if the intersection (sum) of two direct summands of M is also a direct summand. It is shown that the right SIP (SSP) is not a Morita invariant property and that a nonsingular C-11(+)-module does not necessarily have SIP. In contrast, it is shown that the direct sum of two copies of a right Ore domain has SIP as a right module over itself.