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D3-Modules |
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| Authors: | Mohamed Yousif Ismail Amin Yasser Ibrahim |
| Institution: | 1. Department of Mathematics , The Ohio State University , Lima , Ohio , USA yousif.1@osu.edu;3. Faculty of Science, Department of Mathematics , Cairo University , Giza , Egypt |
| Abstract: | A right R-module M is called a D3-module, if M 1 and M 2 are direct summands of M with M = M 1 + M 2, then M 1 ∩ M 2 is a direct summand of M. Following the work of Bass on projective covers, we introduce the notion of D3-covers and provide new characterizations of several well-known classes of rings in terms of D3-modules and D3-covers. |
| Keywords: | D2-modules and D3-modules Discrete and quasi-discrete modules Perfect and semiperfect rings Projective covers and D3-covers Projective and quasi-projective modules Semihereditary and hereditary rings |