Structures of (m,n)-seminearring

Published: 2 April 2024| Version 1 | DOI: 10.17632/vjf88c86gr.1
Muhsang Sudadama Lieko Liedokto


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.


Steps to reproduce

Systematic steps will be taken while working on this article. First, an extensive literature review is conducted to review previous contributions and identify research gaps. Second, understanding the properties of ternary seminearring and (m,n)-semiring structures. Finally, definitions and properties are formulated by adopting existing theories in (m,n)-semiring.


Universitas Negeri Malang Jurusan Matematika


Algebra, Abstract Algebra, Algebraic Structure, Algebraic Logic