Related representation theorems for rings, semi-rings, near-rings and semi-near-rings by partial transformations and partial endomorphisms

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Abstract
Fundamental statements for (associative) rings are that (a) the endomorphisms of each commutative group (U, +) form a ring and (b) eachring may be embedded in such a ring of endomorphisms. In order to generalise these theorems to groups and rings whose addition may not be commutative, one has to deal with partial endomorphisms. But thesering-theoretical Theorems 4a and 4b turn out to be specialisations of similarones for semi-near-rings, near-rings and semirings, developed here inSection 2 after some preliminaries on semi-near-rings in Section 1. A glance at Definition 1 and the ring-theoretical theorems and remarks at the end of Section 2 may give more orientation.

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