Simple-direct-modules |
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| Authors: | Yasser Ibrahim M Tamer Ko?an Truong Cong Quynh |
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| Institution: | 1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt;2. Department of Mathematics, Gebze Technical University, Gebze, Kocaeli, Turkey;3. Department of Mathematics, Danang University, DaNang, Vietnam |
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| Abstract: | A right R-module M is called simple-direct-injective if, whenever, A and B are simple submodules of M with A?B, and B?⊕M, then A?⊕M. Dually, M is called simple-direct-projective if, whenever, A and B are submodules of M with M∕A?B?⊕M and B simple, then A?⊕M. In this paper, we continue our investigation of these classes of modules strengthening many of the established results on the subject. For example, we show that a ring R is uniserial (artinian serial) with J2(R) = 0 iff every simple-direct-projective right R-module is an SSP-module (SIP-module) iff every simple-direct-injective right R-module is an SIP-module (SSP-module). |
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| Keywords: | Artinian serial rings and uniserial rings C3- and D3-modules CS and lifting modules simple-direct-injective and simple-direct-projective modules SSP and SIP modules |
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