On the Imbedding of One Semi-Group in Another, with Application to Semi-Rings
Harry S. Vandiver · American Journal of Mathematics · 1940
In other papers 1 a semi-group was defined as a set of elements closed ander an associative operation and for which the equivalence and the substitution postulates hold. tn the present paper we shall employ instead of the substitution postulate, the postulate that if A = B, then CA = CB and AC = BC for any A, B or C in the set, which we shall call the composition postulate.2 A gruppoid 3 is a semi-group with an identity element, that is, an E such that, AE = EA = A for any A in the set. A quasi-group is a semi-group such that from either of the relations