Peter R. Fuchs,
"A Characterization of Left Regularity"
, in Universal Journal of Mathematics and Applications, Vol. 2, Nummer 1, Dergipark, Seite(n) 11-13, 3-2019, ISSN: 2619-9653
A Characterization of Left Regularity
Sprache des Titels:
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.