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Regularities in Ordered n-Ary Semihypergroups
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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 1≤j≤n and n≥3. 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.
Title: Regularities in Ordered n-Ary Semihypergroups
Description:
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 1≤j≤n and n≥3.
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.
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