On weakly 2-prime ideals in commutative rings

Koç S.

COMMUNICATIONS IN ALGEBRA, vol.49, no.8, pp.3387-3397, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 8
  • Publication Date: 2021
  • Doi Number: 10.1080/00927872.2021.1897133
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3387-3397
  • Keywords: Compactly 2-packed ring, compactly packed ring, coprimely packed ring, 2-prime ideal, weakly 2-prime ideal, weakly prime ideal

Abstract

The purpose of the paper is to introduce and study weakly 2-prime ideals in commutative rings. Let A be a commutative ring with a nonzero identity. A proper ideal P of A is said to be a weakly 2-prime ideal if whenever 0 not equal xy is an element of P for some x, y is an element of A, then x(2) is an element of P or y(2) is an element of P: Besides giving various examples and characterizations of weakly 2-prime ideals, we investigate the relations between weakly 2-prime ideals and other classical ideals such as 2-prime ideals, weakly prime ideals and weakly 2-absorbing primary ideals. Furthermore, we study 2-prime avoidance lemma in commutative rings and introduced the class of compactly 2-packed rings. Finally, we investigate the compactly packedness, compactly 2-packedness and coprimely packedness of trivial extension A (sic) M of an A-module M.