The dual notion of the prime radical of a module

Ceken S., ALKAN M., Smith P. F.

JOURNAL OF ALGEBRA, vol.392, pp.265-275, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 392
  • Publication Date: 2013
  • Doi Number: 10.1016/j.jalgebra.2013.06.015
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.265-275
  • Keywords: Second submodule, Second radical, Prime submodule, Prime radical, Socle of a module, SUBMODULES, RINGS
  • Akdeniz University Affiliated: Yes

Abstract

In this article, we study the second radical of a module over an arbitrary ring R as the dual notion of the prime radical of a module. We give some properties of the second radical and determine the second radical of some modules. We define the notion of m*-system and describe the second radical of submodules in terms of m*-systems. We investigate when the second radical of a module M is equal to the socle of M. In particular, we give a characterization of the socle of a noetherian module over a ring R such that the ring R/P is right artinian for every right primitive ideal P by using the concept of second radical. We also give a characterization of right quasi-duo artinian rings by using the second radical of an injective module. (C) 2013 Elsevier Inc. All rights reserved.