Loop-half-groupoid near-rings (Q1084484)

The authors introduce the class of loop half-groupoid near-rings as a generalization of the class of loop-near-rings, define the \(\Delta\)- centralizer \({\mathcal S}\) of a loop \({\mathcal G}\), \(\Delta\subset {\mathcal G}\), \(\Delta\)-transformation of \({\mathcal G}\) over \({\mathcal S}\), \({\mathcal S}\)- equivalence, \({\mathcal N}\)-loops of type 0,1,2, where \({\mathcal N}\) is a loop- half-groupoid near ring and investigate their relations. The last theorem proves that every 0-primitive loop-near-ring with unity can be densely embedded in a loop-half-groupoid near-ring of transformations.