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On Minimal and Maximal Hyperidealsin n-ary Semihypergroups
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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.
Title: On Minimal and Maximal Hyperidealsin n-ary Semihypergroups
Description:
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.
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