ON PSEUDO 2-PRIME IDEALS AND ALMOST VALUATION DOMAINS

Koç S.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.58, no.4, pp.897-908, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.4134/bkms.b200614
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded, Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.897-908
  • Keywords: Prime ideal, 2-prime ideal, pseudo 2-prime ideal, valuation domain, almost valuation domain, DIVIDED RINGS

Abstract

In this paper, we introduce the notion of pseudo 2-prime ideals in commutative rings. Let R be a commutative ring with a nonzero identity. A proper ideal P of R is said to be a pseudo 2-prime ideal if whenever xy is an element of P for some x, y is an element of R, then x(2n) is an element of P-n or y(2n) is an element of P-n for some n is an element of N. Various examples and properties of pseudo 2-prime ideals are given. We also characterize pseudo 2-prime ideals of PID's and von Neumann regular rings. Finally, we use pseudo 2-prime ideals to characterize almost valuation domains (AV-domains).