Abstract
Abstract In this paper, we study various strongly convex hyper S-subposets of hyper S-posets in detail. To begin with, we consider the decomposition of hyper S-posets. A unique decomposition theorem for hyper S-posets is given based on strongly convex indecomposable hyper S-subposets. Furthermore, we discuss the properties of minimal and maximal strongly convex hyper S-subposets of hyper S-posets. In the sequel, the concept of hyper C-subposets of a hyper S-poset is introduced, and several related properties are investigated. In particular, we discuss the relationship between greatest strongly convex hyper S-subposets and hyper C-subposets of hyper S-posets. Moreover, we introduce the concept of bases of a hyper S-poset and give out the sufficient and necessary conditions of the existence of the greatest hyper C-subposets of a hyper S-poset by the properties of bases.
Highlights
IntroductionThe composition of two elements in a group is an element, whereas the composition of two elements in a hypergroup is a nonempty set
For a semigroup S, a left S-act is a nonempty set A equipped with a mapping S × A → A, (s, a) ⇝ sa, such thata = s(ta) for all a ∈ A and s, t ∈ S
We introduce the concept of bases of a hyper S-poset and give out the sufficient and necessary conditions of the existence of the greatest hyper C-subposets of a hyper S-poset in terms of bases
Summary
The composition of two elements in a group is an element, whereas the composition of two elements in a hypergroup is a nonempty set The law characterizing such a structure is called the multi-valued operation, or hyperoperation and the theory of the algebraic structures endowed with at least one. Tang et al [32] defined and studied the hyper S-posets over an ordered semihypergroup, and extended some results on S-posets to hyper S-posets. We define and investigate the a-maximal strongly convex hyper S-subposets of a hyper S-poset.
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