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An investigation on hyperS-posets over ordered semihypergroups

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Tang J., Davvaz B., Xie X.-Y.

Open Mathematics

2017

tom 15

nr 1

37-56

In this paper, we define and study the hyper S-posets over an ordered semihypergroup in detail. We introduce the hyper version of a pseudoorder in a hyper S-poset, and give some related properties. In particular, we characterize the structure of factor hyper S-posets by pseudoorders. Furthermore, we introduce the concepts of order-congruences and strong order-congruences on a hyper S-poset A, and obtain the relationship between strong order-congruences and pseudoorders on A. We also characterize the (strong) order-congruences by the ρ-chains, where ρ is a (strong) congruence on A. Moreover, we give a method of constructing order-congruences, and prove that every hyper S-subposet B of a hyper S-poset A is a congruence class of one order-congruence on A if and only if B is convex. In the sequel, we give some homomorphism theorems of hyper S-posets, which are generalizations of similar results in S-posets and ordered semigroups.

Ograniczanie wyników

1 Open Mathematics

1 Davvaz B.

1 Tang J.

1 Xie X.-Y.

1 2017

Wyniki wyszukiwania

An investigation on hyperS-posets over ordered semihypergroups