Special Classes of Semigroups
Springer Science & Business Media, 31 mai 2001 - 269 pages
In semigroup theory there are certain kinds of band decompositions, which are very useful in the study of the structure semigroups. There are a number of special semigroup classes in which these decompositions can be used very successfully. The book focuses attention on such classes of semigroups. Some of them are partially discussed in earlier books, but in the last thirty years new semigroup classes have appeared and a fairly large body of material has been published on them. The book provides a systematic review on this subject. The first chapter is an introduction. The remaining chapters are devoted to special semigroup classes. These are Putcha semigroups, commutative semigroups, weakly commutative semigroups, R-Commutative semigroups, conditionally commutative semigroups, RC-commutative semigroups, quasi commutative semigroups, medial semigroups, right commutative semigroups, externally commutative semigroups, E-m semigroups, WE-m semigroups, weakly exponential semigroups, (m,n)-commutative semigroups and n(2)-permutable semigroups.
Audience: Students and researchers working in algebra and computer science.
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0-simple arbitrary elements Assume cancellative semigroup chain with respect commutative archimedean semigroup commutative group commutative nil semigroup containing at least Corollary defined disjoint union E-m semigroup form a chain free semigroup fs(n G or G globally idempotent core group G group homomorphic image Hence ideal extension idempotent element implies inverse semigroup isomorphic least one idempotent left right left zero semigroup Lemma m,n)-commutative semigroup medial semigroup modulo n(2)-permutable nilpotent non-trivial subgroup non-zero disjunctive element permutation function positive integer Proof quasicyclic p-group rectangular abelian group rectangular band Rees congruence Rees factor Rees matrix semigroup regular semigroup respect to inclusion retract extension right commutative semigroup right Putcha semigroup right zero semigroup satisfies the identity semi simple semigroup subdirect product subdirectly irreducible subsemigroup theorem is proved two-element left zero two-element right zero two-element semilattice WE-m weakly commutative semigroup weakly separative congruence zero adjoined zero element