Commutative Semigroups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Springer US
2001
|
| Series: | Advances in Mathematics
2 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 standard examples of semigroups, which consist of various kinds of transformations or arise from finite automata, and are usually quite noncommutative. Commutative semigroups provide a natural setting and a useful tool for the study of factorization 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 semigroups. Commutative results also invite generalization to larger classes of semigroups. Archimedean decompositions, a comparatively small part of today's arsenal, have been generalized extensively, as shown for instance in the upcoming books by Nagy [2001] and Ciric [2002] |
| Physical Description: | 1 Online-Ressource (XIV, 437 p) |
| ISBN: | 9781475733891 9781441948571 |
| DOI: | 10.1007/978-1-4757-3389-1 |
Staff View
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| 500 | |a 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 standard examples of semigroups, which consist of various kinds of transformations or arise from finite automata, and are usually quite noncommutative. Commutative semigroups provide a natural setting and a useful tool for the study of factorization 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 semigroups. Commutative results also invite generalization to larger classes of semigroups. Archimedean decompositions, a comparatively small part of today's arsenal, have been generalized extensively, as shown for instance in the upcoming books by Nagy [2001] and Ciric [2002] | ||
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Record in the Search Index
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475733891 9781441948571 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856878 |
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| physical | 1 Online-Ressource (XIV, 437 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer US |
| record_format | marc |
| series | Advances in Mathematics |
| series2 | Advances in Mathematics |
| spelling | Grillet, P. A. Verfasser aut Commutative Semigroups by P. A. Grillet Boston, MA Springer US 2001 1 Online-Ressource (XIV, 437 p) txt rdacontent c rdamedia cr rdacarrier Advances in Mathematics 2 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 standard examples of semigroups, which consist of various kinds of transformations or arise from finite automata, and are usually quite noncommutative. Commutative semigroups provide a natural setting and a useful tool for the study of factorization 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 semigroups. Commutative results also invite generalization to larger classes of semigroups. Archimedean decompositions, a comparatively small part of today's arsenal, have been generalized extensively, as shown for instance in the upcoming books by Nagy [2001] and Ciric [2002] Mathematics Algebra Group theory Group Theory and Generalizations Mathematik Advances in Mathematics 2 (DE-604)BV025360563 2 https://doi.org/10.1007/978-1-4757-3389-1 Verlag Volltext |
| spellingShingle | Grillet, P. A. Commutative Semigroups Advances in Mathematics Mathematics Algebra Group theory Group Theory and Generalizations Mathematik |
| title | Commutative Semigroups |
| title_auth | Commutative Semigroups |
| title_exact_search | Commutative Semigroups |
| title_full | Commutative Semigroups by P. A. Grillet |
| title_fullStr | Commutative Semigroups by P. A. Grillet |
| title_full_unstemmed | Commutative Semigroups by P. A. Grillet |
| title_short | Commutative Semigroups |
| title_sort | commutative semigroups |
| topic | Mathematics Algebra Group theory Group Theory and Generalizations Mathematik |
| topic_facet | Mathematics Algebra Group theory Group Theory and Generalizations Mathematik |
| url | https://doi.org/10.1007/978-1-4757-3389-1 |
| volume_link | (DE-604)BV025360563 |
| work_keys_str_mv | AT grilletpa commutativesemigroups |