Commutative rings with one-absorbing factorization. Issue 6 (30th January 2021)

• Record Type: Journal Article
• Authors: Khalfi, Abdelhaq El; Issoual, Mohammed; Mahdou, Najib; Reinhart, Andreas
• Is Part Of: Communications in algebra. Volume 49:Issue 6(2021)
• Page Start: 2689
• Page End: 2703
• Publication Date: 2021-01-30
• Subjects: OA-ideal -- OAF-ring -- trivial ring extension; Primary: 13B99 -- Secondary: 13A15 -- 13G05 -- 13B21; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1881105
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let R be a commutative ring with nonzero identity. Yassine et al. defined the concept of 1-absorbing prime ideals as follows: a proper ideal I of R is said to be a 1-absorbing prime ideal if whenever xyz ∈ I for some nonunit elements x, y, z ∈ R, then either x y ∈ I or z ∈ I . We use the concept of 1-absorbing prime ideals to study those commutative rings in which every proper ideal is a product of 1-absorbing prime ideals (we call them OAF -rings). Any OAF -ring has dimension at most one and local OAF -domains ( D, M ) are atomic such that M 2 is universal.