P.g Romeo

Structure of Concordant Semigroups-ii: Cross-connections P.g Romeo

Semigroups are algebraic structures consisting of a non empty set together with an associative binary operation. The theory of semigroups has experienced a vigorous development during the last few decades to become an independent branch of algebra with applications to several branches of mathematics. The theory of semigroups had essentially two origns. One was an attempt to generalize both group theory and to a lesser extent ring theory to a system consisting of a single associative operation and the other consisted of an abstraction of the properties of the composition of transformation on a set. The study of the structure of semigroups grew as a central theme in semigroup research, among the various types of semigroups the class of regular semigroups are those which admits some sort of inverses and their structure theorems are well established. The class of non regular semigroups are less investigated and the present study is an attempt to formulate a structure theorem for concordant semigroups ? an interesting class of non regular semigroups .