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Semigroup Theory: Course Outline (MAT-612)

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.

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Course Outline

Introductory ideas: Basic definitions, Cyclic semigroups; Ordered sets, semi lattices and lattices. Binary relations; Equivalences; Congruences; Free semigroups; Green’s Equivalances; L,R,H,J and D; Regular semigroups, O-Simple semigroups; Simple and O-Simple semigroups; Rees’s theorem; Primative idempotents; Completely O-Simple semigroups; Finite congruence-free semigroups, Union of groups; Bands; Free bands; varieties of bands, Inverse semigroups, Congruences on inverse semigroups; Fundamental inverse semigroups; Bisimple and simple inverse semigroups. Orthodox semigroups; Basic properties; The structure of orthodox semigroups.

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