<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper we provide various properties of Rad-⊕-supplemented modules. In particular, we prove that a projective module M is Rad- ⊕-supplemented if and only if M is ⊕-supplemented, and then we show that a commutative ring R is an artinian serial ring if and only if every left R-module is Rad-⊕-supplemented. Moreover, every left R-module has the property (P*) if and only if R is an artinian serial ring and J<sup>2 </sup>= 0, where J is the Jacobson radical of R. Finally, we show that every Rad-supplemented module is Rad-⊕-supplemented over dedekind domains.</p></abstract>

In this paper we provide various properties of Rad-⊕-supplemented modules. In particular, we prove that a projective module M is Rad- ⊕-supplemented if and only if M is ⊕-supplemented, and then we show that a commutative ring R is an artinian serial ring if and only if every left R-module is Rad-⊕-supplemented. Moreover, every left R-module has the property (P*) if and only if R is an artinian serial ring and J2 = 0, where J is the Jacobson radical of R. Finally, we show that every Rad-supplemented module is Rad-⊕-supplemented over dedekind domains.

Rad-⊕-Supplemented Modules

Department of Mathematics, Amasya University, Ipekkoy, 05100, Amasya, Turkey

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Rad-⊕-Supplemented Modules"}

In this paper we provide various properties of Rad-⊕-supplemented modules. In particular, we prove that a projective module M is Rad- ⊕-supplemented if and...

Rad-⊕-Supplemented Modules

Publié en ligne: 30 juil. 2013

Pages: 225 - 237

DOI: https://doi.org/10.2478/auom-2013-0015

This content is open access.