On right self-injective regular semigroups

On right self-injective regular semigroups, II

“…By Corollary 1.11 of [10], a right self-injective band is right regular. So Corollary 2.10 gives a necessary and sufficient condition for a band to be right self-injective in terms of right ideals and right congruences.…”

“…The "only i f statement follows from Corollary 1.11 of [10]. To prove the " i f statement it suffices to show that E satisfies condition (iii) of Corollary 2.10.…”

“…Also by condition (i), 5 has a zero element. So by applying Theorem 1.12 of [10], we see that it suffices to show that for any right congruence p on 5 and for any right ideal K of S such that kp C K for all k G K, each S-homomorphism \p: Kp^ -» S extends to an S-homomorphism of S/p into S. Let p, K, 4> be as above. Put J = i>(Kp^).…”

“…The author [10] showed that a right self-injective generalized inverse [right //-compatible regular, 0-proper regular] semigroup is right inverse and gave a structure theorem for right self-injective generalized inverse semigroups. In Section 2, we shall state some results on a right self-injective, right inverse semigroup.…”

“…For any subset M of S, M* = U {V(a) a G M). All other notations and terminology should be referred to [1] and [10]. unless otherwise stated.…”