Congruences on Cliford Quasi-Regular Semigroups (Report‪)‬

Abstract Let S be a nil-extension of a Cliford semigroup K by a nil semigroup Q. A congruence pair ([delta], [omega]) on S consists of a congruence [delta] on Q and a congruence [omega] on K. It is proved that there is an order-preserving bijection [TAU] : [sigma] [right arrow] ([[sigma].sub.Q], [[sigma].sub.K]) from the set of all congruences on S onto the set of all congruence pairs on S, where [[sigma].sub.K] is the restriction of [sigma] on K, [[sigma].sub.Q] = ([sigma] V [[rho].sub.K])[[rho].sub.K] and [[rho].sub.K] is the Rees congruence on S induced by K. Keywords Clifford quasi-regular semigroups, Nil-extension, congruence pairs.