Ideals Grzegorz Bancerek Institute of Mathematics Polish Academy

(2) Let D be a non empty set, S be a non empty subset of D, f be a binary operation on D, g be a binary operation on S, d be an element of D, and d′ be an element of S such that g = f [:S, S :] and d′ = d. Then (i) if d is a left unity w.r.t. f , then d′ is a left unity w.r.t. g, (ii) if d is a right unity w.r.t. f , then d′ is a right unity w.r.t. g, and (iii) if d is a unity w.r.t. f , then d′ is a unity w.r.t. g.