Ideal theory of $(m, n)$-near rings

Year 2024, Volume: 73 Issue: 4, 1098 - 1113, 30.12.2024

Fahime Mohammadi Bijan Davvaz

https://doi.org/10.31801/cfsuasmas.1494749

Abstract

The aim of this research work is to define and characterize a new class of $n$-ary algebras that we call $(m,n)$-near rings. We investigate the notions of $i$-$R$-groups, $i$-$(m, n) $-near field, prime ideals, primary ideals and subtractive ideals of $(m,n)$-near rings. We describe the concept of homomorphisms between $ (m, n) $-near rings that preserve the $(m, n)$-near ring structure, and give some results in this respect.

Keywords

(m,n)-near ring , (m,n)-near field , ideal , homomorphism

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