On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings

Kazanci O., Davvaz B.

INFORMATION SCIENCES, vol.178, no.5, pp.1343-1354, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 178 Issue: 5
  • Publication Date: 2008
  • Doi Number: 10.1016/j.ins.2007.10.005
  • Journal Name: INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1343-1354
  • Keywords: fuzzy set, rough set, lower approximation, upper approximation, ring, ideal, prime ideal, primary ideal, fuzzy ideal, APPROXIMATION OPERATORS, SETS, SEMIGROUPS, SUBMODULES, RADICALS, MODULES, LATTICE, VIEW
  • Karadeniz Technical University Affiliated: No

Abstract

This paper is a continuation of ideas presented by Davvaz [Roughness in rings, Inform. Sci., 164 (2004) 147-163; Roughness based on fuzzy ideals, Inform. Sci., 176 (2006) 2417-2437]. We introduce the notions of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in a ring, and give some properties of such ideals. Also, we discuss the relations between the upper and lower rough prime (primary) ideals and the upper and lower approximations of their homomorphism images. (C) 2007 Elsevier Inc. All rights reserved.