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

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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