Journals / Turkish Journal of Mathematics / 2002 / Cilt: 26 - Sayı: 2
On Summand Sum and Summand Intersection Property of Modules
- Pages
- 131–147
- DOI
- —
Abstract
R will be an associative ring with identity and modules M will be unital left R- modules. In this work, extending modules and lifting modules with the SSP (or SIP) are studied. A necessary and sufficient condition for a module M to have the SSP is that for every decomposition M = A\oplus B and f\in Hom(A,B), Im(f) is a direct summand of B. Among others it is shown also that a (C3) module with the SIP has the SSP, and a (D3) module with SSP has the SIP.
Özet
R will be an associative ring with identity and modules M will be unital left R- modules. In this work, extending modules and lifting modules with the SSP (or SIP) are studied. A necessary and sufficient condition for a module M to have the SSP is that for every decomposition M = A\oplus B and f\in Hom(A,B), Im(f) is a direct summand of B. Among others it is shown also that a (C3) module with the SIP has the SSP, and a (D3) module with SSP has the SIP.