Abstract
The notion of ordered semihyperrings is a generalization of ordered semirings and a generalization of semihyperrings. In this paper, the Galois connection between ordered semihyperrings are studied in detail and various interesting results are obtained. A construction of an ordered semihyperring via a regular relation is given. Furthermore, we present the Galois connection between homomorphisms and derivations on an ordered semihyperring.
Highlights
In [1], Rasouli established a connection between stabilizers and Galois connection in residuated lattices
We present the Galois connection between homomorphisms and derivations on an ordered semihyperring
We introduced the notion of Galois connections between ordered semihyperrings and obtained some of their useful properties
Summary
In [1], Rasouli established a connection between stabilizers and Galois connection in residuated lattices. For more details about Galois connections, we refer the reader to Chapter 1 of [2]. Some examples for Galois connections can be found in [2]. Rasouli [1], on Galois connection of stabilizers in residuated lattices, we investigate Galois connections between ordered semihyperrings. Hypergroups were introduced in 1934 by Marty [3] as group generalizations. The notion of hyperrings and hyperfields was introduced by Krasner [4] as a generalization of rings. Hyperrings and hyperfields were introduced by Krasner in connection with his work on valued fields. In [5], Jun studied algebraic and geometric aspects of Krasner hyperrings
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