Generalized Polynomials on Semigroups
This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semi-groups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G generates G in the sense that G = S · S−1, then a genera...
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| Format: | Article |
| Language: | English |
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Sciendo
2024-03-01
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| Series: | Annales Mathematicae Silesianae |
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| Online Access: | https://doi.org/10.2478/amsil-2023-0026 |
| _version_ | 1827298476019417088 |
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| author | Ebanks Bruce |
| author_facet | Ebanks Bruce |
| author_sort | Ebanks Bruce |
| collection | DOAJ |
| description | This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semi-groups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G generates G in the sense that G = S · S−1, then a generalized polynomial on S with values in an Abelian group H can be extended to a generalized polynomial on G into H. Finally there is a short discussion of the extendability of exponential functions and generalized exponential polynomials. |
| first_indexed | 2024-04-24T15:15:29Z |
| format | Article |
| id | doaj.art-f59d1cba21744d7cacf72e0ae8c226a8 |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-04-24T15:15:29Z |
| publishDate | 2024-03-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-f59d1cba21744d7cacf72e0ae8c226a82024-04-02T09:28:47ZengSciendoAnnales Mathematicae Silesianae2391-42382024-03-01381182810.2478/amsil-2023-0026Generalized Polynomials on SemigroupsEbanks Bruce01Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USAThis article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semi-groups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G generates G in the sense that G = S · S−1, then a generalized polynomial on S with values in an Abelian group H can be extended to a generalized polynomial on G into H. Finally there is a short discussion of the extendability of exponential functions and generalized exponential polynomials.https://doi.org/10.2478/amsil-2023-0026homomorphismsemigroupmulti-homomorphismmulti-additive functiongeneralized polynomialextension39b5239b82 |
| spellingShingle | Ebanks Bruce Generalized Polynomials on Semigroups Annales Mathematicae Silesianae homomorphism semigroup multi-homomorphism multi-additive function generalized polynomial extension 39b52 39b82 |
| title | Generalized Polynomials on Semigroups |
| title_full | Generalized Polynomials on Semigroups |
| title_fullStr | Generalized Polynomials on Semigroups |
| title_full_unstemmed | Generalized Polynomials on Semigroups |
| title_short | Generalized Polynomials on Semigroups |
| title_sort | generalized polynomials on semigroups |
| topic | homomorphism semigroup multi-homomorphism multi-additive function generalized polynomial extension 39b52 39b82 |
| url | https://doi.org/10.2478/amsil-2023-0026 |
| work_keys_str_mv | AT ebanksbruce generalizedpolynomialsonsemigroups |