2021/12/08 by Xu, Peng, Meli̇s Bolat, Bolat, Melis +8
Decision Sciences · Mathematics · #13A15 #13C05 #13C13 #FOS: Mathematics #Fuzzy and Soft Set Theory #General Mathematics (math.GM) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2112.05513
openalex publication_date 2021/12/08 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
In this paper, our purpose is to define the expansion of r-hyperideals and extend this concept to ϕ-δ-r-hyperideal. Let \Re be a commutative Krasner hyperring with nonzero identity. Given an expansion δ of hyperideals, a proper hyperideal N of \Re is called δ-r-hyperideal if a⋅ b∈ N with ann(a)=0 implies that b∈ δ(N), for all a,b∈\Re. Therefore, given an expansion δ of hyperideals and a hyperideal reduction ϕ, a proper hyperideal N of \Re is called ϕ-δ-r-hyperideal if a⋅ b∈ N-ϕ(N) with ann(a)=0 implies that b∈δ(N), for all a,b∈\Re. We investigate some of their properties and give some examples.