Special Classes of SemigroupsSpringer Science & Business Media, 2001. máj. 31. - 269 oldal 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 A-semigroup arbitrary elements Assume cancellative semigroup chain with respect commutative archimedean semigroup commutative group commutative nil semigroup conditionally commutative semigroup containing at least Corollary defined disjoint union E-m semigroup form a chain fs(n globally idempotent core group G group homomorphic Hence ideal extension idempotent element identity element implies isomorphic k₁ least one idempotent left right left zero semigroup Lemma medial semigroup modulo n(2)-permutable semigroup n)-commutative semigroup nilpotent non-trivial group homomorphic non-trivial subgroup non-zero disjunctive element permutation function positive integer Proof quasicyclic p-group R-commutative rectangular abelian group rectangular band Rees congruence Rees matrix semigroup regular semigroup respect to inclusion retract extension right commutative semigroup right Putcha semigroup right zero semigroup 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 zero adjoined zero element