- Turkish Journal of Mathematics
- Vol: 26 Issue: 2
- On Summand Sum and Summand Intersection Property of Modules
On Summand Sum and Summand Intersection Property of Modules
Authors : Mustafa Alkan, Abdullah Harmanci
Pages : 131-148
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Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : SIP modules, SSP modules, extending modules, lifting modules.