(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup
We prove that the (b, c)-inverse and the inverse along an element in a semigroup are actually genuine inverse when considered as morphisms in the Schützenberger category of a semigroup. Applications to the Reverse Order Law are given.
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2021-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | https://cgasa.sbu.ac.ir/article_101196_32512c4c16fbf43da33f37078eb2c748.pdf |
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doaj-c2504b10eddc4a79a9853a904bb5388c2021-08-10T19:07:34ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612021-07-0115125527210.52547/cgasa.15.1.255101196(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroupXavier MARY0Laboratoire Modal’X, Université Paris Nanterre, FranceWe prove that the (b, c)-inverse and the inverse along an element in a semigroup are actually genuine inverse when considered as morphisms in the Schützenberger category of a semigroup. Applications to the Reverse Order Law are given.https://cgasa.sbu.ac.ir/article_101196_32512c4c16fbf43da33f37078eb2c748.pdfgeneralized inversesgreen’s relationsreverse order law |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xavier MARY |
| spellingShingle |
Xavier MARY (b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup Categories and General Algebraic Structures with Applications generalized inverses green’s relations reverse order law |
| author_facet |
Xavier MARY |
| author_sort |
Xavier MARY |
| title |
(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup |
| title_short |
(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup |
| title_full |
(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup |
| title_fullStr |
(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup |
| title_full_unstemmed |
(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup |
| title_sort |
(b, c)-inverse, inverse along an element, and the schützenberger category of a semigroup |
| publisher |
Shahid Beheshti University |
| series |
Categories and General Algebraic Structures with Applications |
| issn |
2345-5853 2345-5861 |
| publishDate |
2021-07-01 |
| description |
We prove that the (b, c)-inverse and the inverse along an element in a semigroup are actually genuine inverse when considered as morphisms in the Schützenberger category of a semigroup. Applications to the Reverse Order Law are given. |
| topic |
generalized inverses green’s relations reverse order law |
| url |
https://cgasa.sbu.ac.ir/article_101196_32512c4c16fbf43da33f37078eb2c748.pdf |
| work_keys_str_mv |
AT xaviermary bcinverseinversealonganelementandtheschutzenbergercategoryofasemigroup |
| _version_ |
1721211879347453952 |