On Factorizable Semihypergroups (original) (raw)
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European Journal of Combinatorics, 2015
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Symmetry, 2019
In this paper, we introduce and characterize the breakable semihypergroups, a natural generalization of breakable semigroups, defined by a simple property: every nonempty subset of them is a subsemihypergroup. Then, we present and discuss on an extended version of Rédei’s theorem for semi-symmetric breakable semihypergroups, proposing a different proof that improves also the theorem in the classical case of breakable semigroups.
On Neutro-LA-semihypergroups and Neutro-Hv-LA-semigroups
In this paper, we extend the notion of LA-semihypergroups (resp. Hv-LA-semigroups) to neutro-LA-semihypergroups (respectively, neutro-Hv-LA-semigroups). Anti-LA-semihypergroups (respectively, anti-Hv-LA-semigroups) are studied and investigated some of their properties. We show that these new concepts are different from classical concepts by several examples.
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In this paper, we introduce a generalized class of an Hv-semigroup obtained from an LA-semigroup H. This generalized Hv-structure is called an Hv-LA-semigroup. We provide several examples of Hv-LA-semigroups. Moreover, with the help of an example we obtain that each LA-semigroup endowed with an equivalence relation can induce an Hv-LA-semigroup. We also investigate isomorphism theorems with the help of regular relations. At the end, we introduce the concept of hyperideal and hyperorder in Hv-LAsemigroups and prove some useful results on it.