International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2557

Full Length Research Paper

Some properties of Rad-supplemented modules

Ergül TÜRKMEN1* and Ali PANCAR2
  1Amasya University, Faculty of Arts and Science, Department of Mathematics, 05100 Amasya/TÜRKÄ°YE. 2Ondokuz Mayis University, Faculty of Arts and Science, Department of Mathematics, 55200-Samsun/TURKEY.
Email: [email protected]

  •  Accepted: 06 December 2011
  •  Published: 23 December 2011

Abstract

 

No doubt, a notion of the Rad-supplemented modules can constitute a very important situation in the module theory, because of a generalization of the notion of supplemented modules. Therefore, our work presents a key role mainly in some properties and characterizations of Rad-supplement submodules and Rad-supplemented modules. In this paper, we show that, for a duo module M =  QUOTE  , M is Rad-supplemented if and only if each Mi is Rad-supplemented. Moreover, we prove that if an R-module M contains an artinian submodule N, M is Rad-supplemented if and only if   QUOTE   is Rad-supplemented. In addition, a left hereditary ring R is Rad-supplemented if and only if it is semiperfect, and if the ring is commutative, R is artinian if and only if every left R-module is (amply) Rad-supplemented. We also provide various properties of semilocal modules.

 

Key words: Rad-supplement, Rad-supplemented module, semiperfect ring, artinian ring.