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

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.