Structures of (m,n)-seminearring

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.