Isomorphism Theorems in the Primary Categories of Krasner Hypermodules

Author:

Shojaei HosseinORCID,Fasino DarioORCID

Abstract

Let R be a Krasner hyperring. In this paper, we prove a factorization theorem in the category of Krasner R-hypermodules with inclusion single-valued R-homomorphisms as its morphisms. Then, we prove various isomorphism theorems for a smaller category, i.e., the category of Krasner R-hypermodules with strong single-valued R-homomorphisms as its morphisms. In addition, we show that the latter category is balanced. Finally, we prove that for every strong single-valued R-homomorphism f : A → B and a ∈ A , we have K e r ( f ) + a = a + K e r ( f ) = { x ∈ A ∣ f ( x ) = f ( a ) } .

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

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