Keskin Tütüncü, D., Ertaş Orhan, N., Smith, P. F. and Tribak, R. (2014) Some rings for which the cosingular submodule of every module is a direct summand. Turkish Journal of Mathematics, 38, pp. 649-657. (doi: 10.3906/mat-1210-15)
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Abstract
The submodule Z(M) = ∩{N | M/N is small in its injective hull} was introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P ) if Z(M) is a direct summand of M for every R-module M . It is shown that a commutative perfect ring R has (P ) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M ∈ Mod−R | ZR(M) = 0} is closed under factor modules, then R has (P ) if and only if the ring R is von Neumann regular.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Smith, Professor Patrick |
| Authors: | Keskin Tütüncü, D., Ertaş Orhan, N., Smith, P. F., and Tribak, R. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Turkish Journal of Mathematics |
| Publisher: | Scientific and Technical Research Council of Turkey |
| ISSN: | 1300-0098 |
| ISSN (Online): | 1303-6149 |
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