2024/08/22 by Mahdi Anbarloei, Anbarloei, Mahdi
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2408.12241
openalex publication_date 2024/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Among many generalizations of primary hyperideals, weakly n-ary primary hyperideals and n-ary S-primary hyperideals have been studied recently. Let S be an n-ary multiplicative set of a commutative Krasner (m,n)-hyperring K and, ϕ and δ be reduction and expansion functions of hyperideals of K, respectively. The purpose of this paper is to introduce n-ary ϕ-δ-S-primary hyperideals which serve as an extension of S-primary hyperideals with the help of ϕ and δ. We present some main results and examples explaining the sructure of this concept. We examine the relations of n-ary S-primary hyperideals with other classes of hyperideals and give some ways to connect them. Moreover, we give some characterizations of this notion on direct product of commutative Krasner (m, n)-hyperrings.