A Characterization of Left Regularity

Year 2019, Volume: 2 Issue: 1, 11 - 13, 20.03.2019

Peter Fuchs

https://doi.org/10.32323/ujma.469745

Abstract

We show that a zero-symmetric near-ring $N$ is left regular if and only if $N $ is regular and isomorphic to a subdirect product of integral near-rings, where each component is either an Anshel-Clay near-ring or a trivial integral near-ring. We also show that a zero-symmetric near-ring is regular without nonzero nilpotent elements if and only if the multiplicative semigroup of N is a union of disjoint groups.

Keywords

Anshel-Clay near-ring, Integral near-ring, Left regular, Regular

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