2021/07/09 by Mashhoor Refai, Rashid Abu-Dawwas, Refai, Mashhoor +9
Mathematics · #13A02 #16W50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2107.04659
openalex publication_date 2021/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a group, R be a G-graded commutative ring with nonzero unity\nand GI(R) be the set of all graded ideals of R. Suppose that\n\φ:GI(R)\→ GI(R)\∪ \∅ is a function. In this article,\nwe introduce and study the concept of graded \φ-1-absorbing prime ideals.\nA proper graded ideal I of R is called a graded \φ% -1-absorbing\nprime ideal of R if whenever a,b,c are homogeneous nonunit elements of R\nsuch that abc\∈ I-\φ(I), then ab\∈ I or c\∈ I. Several properties of\ngraded \φ-1-absorbing prime ideals have been examined.\n