Structures of $(m,n)$-seminearring

TL;DR

This paper introduces the concept of $(m, n)$-seminearring, a generalization of $(m, n)$-semiring, and develops foundational theories and properties for this new algebraic structure.

Contribution

It defines $(m, n)$-seminearring, explores its substructures, ideals, homomorphisms, and factor constructions, extending the theory of $(m, n)$-semiring.

Findings

Defined $(m, n)$-seminearring and related concepts

Established properties and homomorphism theories

Constructed factor $(m, n)$-seminearrings

Abstract

This article introduces the $m, n)$-seminearring structure, which is a generalization of $(m, n)$-semiring. This research aims to develop theories of $(m, n)$-seminearring. In particular, the concepts of $(m, n)$-seminearring, $(m, n)$-subseminearring, $(m, n)$-ideal, $(m, n)$-seminearring with unity, homomorphism of $(m, n)$-seminearrings, construction of factor $(m, n)$-seminearring of $(m, n)$-seminearring by congruence relation, and some of its exciting properties are given. The method used in this study is to adopt the theory in $(m, n)$-semiring.