J. Appl. Math. & Computing Vol. 12(2003), No. 1 - 2, pp. 261 - 266 STRUCTURE OF COEXTENSIONS OF REGULAR SEMIGROUPS BY RECTANGULAR BANDS V.M.CHANDRASEKARAN Abstract. In this paper, we described the structure of coextensions of regular semigroups by rectangular bands. AMS Mathematics Subject Classification: 20M17. Keywords and Phrases: Regular semigroup, Coextension, rectangular band 1. Introduction This paper is a continuation of the previous paper [1]. The structure of orthodox semigroups has been studied in [1] by using the technique in the paper [3] . In this paper, we use the same technique to study the structure of coextensions os regular semigroups by rectangular bands. Since an orthodox semigroup is a coextension of inverse semigroup by rectangular bands this result generalises [1]. 2. Preliminaries We use whenever possible the notation of Howie [2]. We also use the following results. Definition 1 [5, p.82]. Let S be regular semigroup. Then a coextension of S is pair (T,θ) where T is a regular semigroup and θ is a homomorphism of T onto S. Definition 2 [4, p.1]. A coextension (T,θ) of S is called a coextension of S by rectangular bands if eθ −1 = {f ∈ T : fθ = e} is rectangular subband of T for each e ∈ E(S). Received July 15, 2002. Revised October 28, 2002. c  2003 Korean Society for Computational & Applied Mathematics. 261