Abstract
The concept of a \(\Gamma \)-semihyperring is a generalization of a semiring, a generalization of a semihyperring and a generalization of a \(\Gamma \)-semiring. In this paper, we introduce the notion of \(\Gamma \)-semihyperring, then we prove some results in this respect and present several examples of \(\Gamma \)-semihyperrings. The notions of ideal and homomorphism are introduced and some properties of them are presented. Moreover, we study some properties of regular and strongly regular relations on a \(\Gamma \)-semihypergroup.
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