ON STRONGLY QUASI PRIMARY IDEALS


Koç S. , Tekir Ü., Ulucak G.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.56, no.3, pp.729-743, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.4134/bkms.b180522
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.729-743
  • Keywords: valuation domain, divided ring, strongly quasi primary ideal, zero divisor graph, ideal based zero divisor graph, ZERO-DIVISOR GRAPH

Abstract

In this paper, we introduce strongly quasi primary ideals which is an intermediate class of primary ideals and quasi primary ideals. Let R be a commutative ring with nonzero identity and Q a proper ideal of R. Then Q is called strongly quasi primary if ab is an element of Q for a, b is an element of R implies either a(2) is an element of Q or b( )(n)is an element of Q (a(n) is an element of Q or b(2) is an element of Q) for some n is an element of N. We give many properties of strongly quasi primary ideals and investigate the relations between strongly quasi primary ideals and other classical ideals such as primary, 2-prime and quasi primary ideals. Among other results, we give a characterization of divided rings in terms of strongly quasi primary ideals. Also, we construct a subgraph of ideal based zero divisor graph Gamma(I) (R) and denote it by Gamma(I)*(R), where I is an ideal of R. We investigate the relations between Gamma(I)*(R) and Gamma(I) (R). Further, we use strongly quasi primary ideals and Gamma(I)*(R) to characterize von Neumann regular rings.