Structures of (m,n)-seminearring

Abstract

In this article, the structure of (𝑚,𝑛)-seminearring is introduced which is a generalization of (𝑚,𝑛)-semiring. The purpose of this research is to develop some theories of (𝑚,𝑛)-seminearring. In particular, the concepts of (𝑚,𝑛)-seminearring, (𝑚,𝑛)-subseminearring, (𝑚,𝑛)-ideal, (𝑚,𝑛)-seminearring with unit, homomorphisms of (𝑚,𝑛)-seminearring, construction of (𝑚,𝑛)-seminearring factor of (𝑚,𝑛)-seminearring by congruence relation, and some of its interesting properties are given. The method used in this study is to adopt the theory in (𝑚,𝑛)-semiring.