Amply weak semisimple-supplemented modules

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Mutlu F. T.

International Journal of Pure and Applied Mathematics, vol.83, no.4, pp.613-621, 2013 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 83 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.12732/ijpam.v83i4.10
  • Journal Name: International Journal of Pure and Applied Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.613-621
  • Keywords: Amply weak semisimple-supplemented module, Supplement submodule, Weak semisimple-supplement submodule
  • Anadolu University Affiliated: Yes

Abstract

Let R be a ring and M be a right R-module. In this paper we will study various properties of amply weak semisimple-supplemented module. It is shown that: (1) every projective weakly semisimple-supplemented module is amply weak semisimple-supplemented; (2) if M is an amply weak semisimplesupplemented module and satisfies DCC on weak semisimple-supplement submodules and on small submodules, then M is Artinian; (3) an amply weak semisimple-supplemented module behaves well with respect to supplements and to homomorphic images. © 2013 Academic Publications, Ltd.