On \(P_k\) and \(P_k'\) near-rings. (English) Zbl 0998.16033
The authors call a (right distributive) nearring \(N\) a \(P_k(r,m)\) nearring, \(P_k'(r,m)\) nearring, respectively, if \(x^kN=x^rNx^m\), \(Nx^k=x^rNx^m\), for all \(x\in N\), respectively, where \(k,r,m\) are natural numbers. If \(r=m=1\) the respective classes are denoted by \(P_k\) and \(P_k'\). Also considered are \(S_r\) and \(S_r'\) nearrings, they have the property that \(x\in Nx^r\), \(x\in x^rN\) for all \(x\in N\), respectively.
Various properties of such nearrings are derived. Examples are given to show that the concepts do not all coincide.
Various properties of such nearrings are derived. Examples are given to show that the concepts do not all coincide.
Reviewer: Hubert Kiechle (Hamburg)
MSC:
16Y30 | Near-rings |