Derivations and relation modules for inverse semigroups
We define the derivation module for a homomorphism of inverse semigroups, generalizing a construction for groups due to Crowell. For a presentation map from a free inverse semigroup, we can then define its relation module as the kernel of a canonical map from the derivation module to the augmentati...
Збережено в:
| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2011
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154764 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Derivations and relation modules for inverse semigroups / N.D. Gilbert// Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 1–19. — Бібліогр.: 23 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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dspace |
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irk-123456789-1547642019-06-16T01:32:11Z Derivations and relation modules for inverse semigroups Gilbert, N.D. We define the derivation module for a homomorphism of inverse semigroups, generalizing a construction for groups due to Crowell. For a presentation map from a free inverse semigroup, we can then define its relation module as the kernel of a canonical map from the derivation module to the augmentation module. The constructions are analogues of the first steps in the Gruenberg resolution obtained from a group presentation. We give a new proof of the characterization of inverse monoids of cohomological dimension zero, and find a class of examples of inverse semigroups of cohomological dimension one. 2011 Article Derivations and relation modules for inverse semigroups / N.D. Gilbert// Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 1–19. — Бібліогр.: 23 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:20M18,20M50,18G20. http://dspace.nbuv.gov.ua/handle/123456789/154764 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We define the derivation module for a homomorphism of inverse semigroups, generalizing a construction for groups due to Crowell. For a presentation map from a free inverse semigroup, we can then define its relation module as the kernel of a canonical map from the derivation module to the augmentation module. The constructions are analogues of the first steps in the Gruenberg resolution obtained from a group presentation. We give a new proof of the characterization of inverse monoids of cohomological dimension zero, and find a class of examples of inverse semigroups of cohomological dimension one. |
| format |
Article |
| author |
Gilbert, N.D. |
| spellingShingle |
Gilbert, N.D. Derivations and relation modules for inverse semigroups Algebra and Discrete Mathematics |
| author_facet |
Gilbert, N.D. |
| author_sort |
Gilbert, N.D. |
| title |
Derivations and relation modules for inverse semigroups |
| title_short |
Derivations and relation modules for inverse semigroups |
| title_full |
Derivations and relation modules for inverse semigroups |
| title_fullStr |
Derivations and relation modules for inverse semigroups |
| title_full_unstemmed |
Derivations and relation modules for inverse semigroups |
| title_sort |
derivations and relation modules for inverse semigroups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154764 |
| citation_txt |
Derivations and relation modules for inverse semigroups / N.D. Gilbert// Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 1. — С. 1–19. — Бібліогр.: 23 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT gilbertnd derivationsandrelationmodulesforinversesemigroups |
| first_indexed |
2023-05-20T17:45:19Z |
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2023-05-20T17:45:19Z |
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1796154011208908800 |