2020/02/28 by Ayman Badawı, Badawi, Ayman, Ece Yetki̇n Çeli̇kel +1
Mathematics · #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2002.12608
openalex publication_date 2020/02/28 · openalex created_date 2020/09/14 · openalex updated_date 2026/07/28
Let R be a commutative ring with 1≠0. In this paper, we introduce the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal. A proper ideal I of R is called a weakly 1-absorbing primary ideal if whenever nonunit elements a,b,c∈ R and 0≠ abc∈ I, then ab∈ I or c∈√(I). A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. Furthermore, we give the correct version of a result on 1-absorbing ideals of commutative rings.