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Keywords = j-hyperideal

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21 pages, 314 KB  
Article
Regularities in Ordered n-Ary Semihypergroups
by Jukkrit Daengsaen and Sorasak Leeratanavalee
Mathematics 2021, 9(16), 1857; https://doi.org/10.3390/math9161857 - 5 Aug 2021
Cited by 8 | Viewed by 2421
Abstract
This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means of j-hyperideals for all positive integers 1jn and n3. We first introduce the notion of (softly) left [...] Read more.
This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means of j-hyperideals for all positive integers 1jn and n3. We first introduce the notion of (softly) left regularity, (softly) right regularity, (softly) intra-regularity, complete regularity, generalized regularity of ordered n-ary semihypergroups and investigate their related properties. Several characterizations of them in terms of j-hyperideals are provided. Finally, the relationships between various classes of regularities in ordered n-ary semihypergroups are also established. Full article
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17 pages, 331 KB  
Article
On Minimal and Maximal Hyperidealsin n-ary Semihypergroups
by Jukkrit Daengsaen, Sorasak Leeratanavalee and Bijan Davvaz
Mathematics 2020, 8(10), 1656; https://doi.org/10.3390/math8101656 - 25 Sep 2020
Cited by 10 | Viewed by 2250
Abstract
The concept of j-hyperideals, for all positive integers 1jn and n2, in n-ary semihypergroups, is a generalization of the concept of left, lateral and right hyperideals in ternary semihypergroups. In this paper, we first [...] Read more.
The concept of j-hyperideals, for all positive integers 1jn and n2, 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. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2020)
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