A near-ring N is said to be strongly reduced if, for a N, implies , where denotes the constant part of N. We investigate some properties of strongly reduced near-rings and apply those to the study of left strongly regular near-rings. Finally we classify all reduced and strongly reduced near-rings of order 7 using the description given in J. R. Clay .
left strongly regular near-rings;strongly reduced near-rings;periodic near-rings;
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