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.
Anshel-Clay near-ring Integral near-ring Left regular Regular
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 20 Mart 2019 |
Gönderilme Tarihi | 12 Ekim 2018 |
Kabul Tarihi | 6 Aralık 2018 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 1 |
Universal Journal of Mathematics and Applications
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