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Zbl 1197.20062
Heidari, Dariush; Dehkordi, Sohrab Ostadhadi; Davvaz, Bijan
$\Gamma$-semihypergroups and their properties. (English)
[J] Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 72, No. 1, 195-208 (2010). ISSN 1223-7027

Summary: Algebraic hyperstructures are a suitable generalization of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of $\Gamma$-semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of $\Gamma$-semigroups. In this paper, we define the notion of ideal, prime ideal, extension of an ideal in $\Gamma$-semihypergroups, then we prove some results in this respect and present many examples of $\Gamma$-semihypergroups. We also introduce the notion of quotient $\Gamma$-semihypergroup by using a congruence relation, and introduce the notion of right Noetherian $\Gamma$-semihypergroups. Finally, we study some properties of fundamental relations on a special kind of $\Gamma$-semihypergroups.

MSC 2000:: *20N20 Hypergroups (group theory)
20M99 Semigroups
20M12 Ideal theory of semigroups

Keywords: semihypergroups; $\Gamma$-semigroups; $\Gamma$-semihypergroups; hypergroups; fundamental relations; prime ideals; extensions of ideals; congruences

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