A Characterization of Left Regularity

Authors : Peter FUCHS

Pages : 11-13

Doi:10.32323/ujma.469745

View : 9 | Download : 11

Publication Date : 2019-03-20

Article Type : Research Paper

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