Commutative Semigroups

P. A. Grillet

ISBN 10: 0792370678 / ISBN 13: 9780792370673

Edité par Springer US, Springer US Jul 2001, 2001

A propos de cet article

Neuware -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].Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 456 pp. Englisch.

N° de réf. du vendeur 9780792370673

Détails bibliographiques

• Titre: Commutative Semigroups
• Éditeur: Springer US, Springer US Jul 2001
• Date de parution: 2001
• Langue: anglais
• ISBN à 10 chiffres: 0792370678
• ISBN à 13 chiffres: 9780792370673
• Reliure: Buch
• État de l'article: Neu

A propos de ce titre

Synopsis

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].