SS-LIFTING MODULES AND RINGS

Eryılmaz F.

MISKOLC MATHEMATICAL NOTES, vol.22, no.2, pp.655-662, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.18514/mmn.2021.3245
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.655-662
  • Keywords: semisimple module, ss-supplemented module, strongly local module
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

A module M is called ss-lifting if for every submodule A of M, there is a decomposition M = M-1 circle plus M-2 such that M-1 <= A and A boolean AND M-2 subset of SOCs (M), where Soc(s) (M) = Soc(M) boolean AND Rad(M). In this paper, we provide the basic properties of ss-lifting modules. It is shown that: (1) a module M is ss-lifting iff it is amply ss-supplemented and its ss-supplement submodules are direct summand; (2) for a ring R, R-R is ss-lifting if and only if it is ss-supplemented iff it is semiperfect and its radical is semisimple; (3) a ring R is a left and right artinian serial ring and Rad (R) subset of Soc (R-R) iff every left R-module is ss-lifting. We also study on factor modules of ss-lifting modules.