ON 2-ABSORBING PRIMARY AND WEAKLY 2-ABSORBING ELEMENTS IN MULTIPLICATIVE LATTICES

ÇALLIALP F., Yetkin E., TEKİR Ü.

ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, no.34, pp.263-276, 2015 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2015
  • Journal Name: ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.263-276
  • Keywords: prime element, primary element, 2-absorbing element, 2-absorbing primary element, multiplicative lattice, COMMUTATIVE RINGS, IDEALS
  • Marmara University Affiliated: Yes

Abstract

In this paper, we introduce the concept of 2-absorbing primary and weakly 2-absorbing primary elements which are generalizations of primary and weakly primary elements in multiplicative lattices. Let L be a multiplicative lattice. A proper element q of L is said to be a (weakly) 2-absorbing primary element of L if whenever a, b, c is an element of L with (0 not equal abc <= q) abc <= q implies either ab <= q or ac <= root q or bc <= root q. Some properties of 2-absorbing primary and weakly 2-absorbing primary elements are presented and relations among prime, primary, 2-absorbing, weakly 2-absorbing, 2-absorbing primary and weakly 2-absorbing primary elements are investigated. Furthermore, we determine 2-absorbing primary elements in some special lattices and give a new characterization for principal element domains in terms of 2-absorbing primary elements.