Commutative Semigroups

P. A. Grillet

ISBN 10: 1441948570 / ISBN 13: 9781441948571

Editore: Springer, Springer, 2010

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Druck auf Anfrage Neuware - Printed after ordering - The first book on commutative semigroups was Redei's The theory of .finitely generated commutative semigroups, published in Budapest in 1956. Subsequent years have brought much progress. By 1975 the structure of finite commutative semigroups was fairly well understood. Recent results have perfected this understanding and extended it to finitely generated semigroups. Today's coherent and powerful structure theory is the central subject of the present book. 1. Commutative semigroups are more important than is suggested by the stan dard examples ofsemigroups, which consist ofvarious kinds oftransformations or arise from finite automata, and are usually quite noncommutative. Commutative of factoriza semigroups provide a natural setting and a useful tool for the study tion in rings. Additive subsemigroups of N and Nn have close ties to algebraic geometry. Commutative rings are constructed from commutative semigroups as semigroup algebras or power series rings. These areas are all subjects of active research and together account for about half of all current papers on commutative semi groups. Commutative results also invite generalization to larger classes of semigroups. Archimedean decompositions, a comparatively small part oftoday's arsenal, have been generalized extensively, as shown for instance in the upcoming books by Nagy [2001] and Ciric [2002].

Codice articolo 9781441948571

Dati bibliografici

• Titolo: Commutative Semigroups
• Editore: Springer, Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 1441948570
• ISBN 13: 9781441948571
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 25 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 25 millimetri di profondità
• Peso: 686 grammi

Descrizione articolo

Riassunto

The first book on commutative semigroups was Redei's The theory of .finitely generated commutative semigroups, published in Budapest in 1956. Subsequent years have brought much progress. By 1975 the structure of finite commutative semigroups was fairly well understood. Recent results have perfected this understanding and extended it to finitely generated semigroups. Today's coherent and powerful structure theory is the central subject of the present book. 1. Commutative semigroups are more important than is suggested by the stan­ dard examples ofsemigroups, which consist ofvarious kinds oftransformations or arise from finite automata, and are usually quite noncommutative. Commutative of factoriza­ semigroups provide a natural setting and a useful tool for the study tion in rings. Additive subsemigroups of N and Nn have close ties to algebraic geometry. Commutative rings are constructed from commutative semigroups as semigroup algebras or power series rings. These areas are all subjects of active research and together account for about half of all current papers on commutative semi groups. Commutative results also invite generalization to larger classes of semigroups. Archimedean decompositions, a comparatively small part oftoday's arsenal, have been generalized extensively, as shown for instance in the upcoming books by Nagy [2001] and Ciric [2002].

Contenuti

Preface. General structure theory: I. Elementary properties. II. Cancellative semigroups. III. Semilattice decompositions. IV. Subdirect decompositions. V. Group coextensions. VI. Finitely generated semigroups. VII. Subcomplete semigroups. VIII. Other results. Congruences: IX. Nilsemigroups. X. Group-free semigroups. XI. Subcomplete semigroups. Cohomology: XII. Commutative semigroup cohomology. XIII. The overpath method. XIV. Semigroups with zero cohomology. References. Author. Index. Notation. Index.