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On Corsini hypergroups and their productional hypergroups
M. Al Tahan,B. Davvaz 강원경기수학회 2019 한국수학논문집 Vol.27 No.1
In this paper, we consider a special hypergroup defined by Corsini and we name it Corsini hypergroup. First, we investigate some of its properties and find a necessary and sufficient condition for the productional hypergroup of Corsini hypergroups to be a Corsini hypergroup. Next, we study its regular relations, fundamental group and complete parts. Finally, we characterize all Corsini hypergroups of orders two and three up to isomorphism.
On Isomorphism Theorems and Chinese Remainder Theorem in Hypernear Rings
M. Al Tahan,B. Davvaz 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.4
The purpose of this paper is to consider the abstract theory of hypernear rings. In this regard, we derive the isomorphism theorems for hypernear rings as well as Chinese Remainder theorem. Our results can be considered as a generalization for the cases of Krasner hyperrings, near rings, and rings.