Publications de l'Institut Mathématique, Nouvelle SérieVol. 99(113), pp. 249–255 (2016)
|
|
Publications de l'Institut Mathématique, Nouvelle Série Vol. 99(113), pp. 249–255 (2016) |
|
|
ON GENERALIZATION OF INJECTIVE MODULESBurcu NisanciTürkmenFaculty of Art and Science, Amasya University, Amasya, TurkeyAbstract: As a proper generalization of injective modules in term of supplements, we say that a module $M$ has \emph{the property} (SE) (respectively, \emph{the property} (SSE)) if, whenever $M\subseteq N$, $M$ has a supplement that is a direct summand of $N$ (respectively, a strong supplement in $N$). We show that a ring $R$ is a left and right artinian serial ring with $\operatorname{Rad}(R)^2=0$ if and only if every left $R$-module has the property (SSE). We prove that a commutative ring $R$ is an artinian serial ring if and only if every left $R$-module has the property (SE). Keywords: supplement; module with the properties (SE) and (SSE); artinian serial ring Classification (MSC2000): 16D10; 16D50 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 12 Apr 2016. This page was last modified: 20 Apr 2016.
© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
|