JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 3, Pages 469 - 490
(December 2005)
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CHARACTERIZATION OF MODULES AND RINGS BY THE SUMMAND INTERSECTION PROPERTY AND THE SUMMAND SUM PROPERTY
A. Hamdouni (Tunisie), A. Ç® Öºcan (Turkey) and A. Harmanci (Turkey)
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Abstract: R will be a ring with identity and modules M will be unital right R-modules. In this paper, properties of modules having the summand intersection property (SIP) and the summand sum property (SSP) are studied. We study the direct sum of modules, the SIP and the SSP. We add some results concerning characterization of some rings by means of modules having the SIP or the SSP. |
Keywords and phrases: semisimple module, injective module, projective module, injective hull, SIP modules, SSP modules, prime module, divisible module, torsion free module, (semi-) hereditary ring, semisimple ring, V-ring, finitely cogenerated module, finitely copresented module. |
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