On Minimal and Maximal Hyperidealsin n -ary Semihypergroups

Jukkrit Daengsaen, Sorasak Leeratanavalee and Bijan Davvaz
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Jukkrit Daengsaen: PhD Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Sorasak Leeratanavalee: Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Bijan Davvaz: Department of Mathematics, Yazd University, Yazd 89139, Iran

Mathematics, 2020, vol. 8, issue 10, 1-17

Abstract: The concept of j -hyperideals, for all positive integers 1 ≤ j ≤ n and n ≥ 2 , in n -ary semihypergroups, is a generalization of the concept of left, lateral and right hyperideals in ternary semihypergroups. In this paper, we first introduce the concept of j -(0-)simple n -ary semihypergroups and discuss their related properties through terms of j -hyperideals. Furthermore, we characterize the minimality and maximality of j -hyperideals in n -ary semihypergroups and establish the relationships between the (0-)minimal, maximal j -hyperideals and the j -(0-)simple n -ary semihypergroups. Our main results are to extend and generalize the results on semihypergroups and ternary semihypergroups. Moreover, a related question raised by Petchkaew and Chinram is solved.

Keywords: semihypergroup; n-ary semihypergroup; hyperideal; j-hyperideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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