Generalized polynomials on semigroups

Bruce Ebanks

Published: 2024-01-10

Vol. 38 No. 1 (2024)

Generalized polynomials on semigroups

Bruce Ebanks

Abstract

This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semigroups 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.

Keywords:

homomorphism , semigroup , multi-homomorphism , multiadditive function , generalized polynomial , extension

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Ebanks, B. (2024). Generalized polynomials on semigroups. Annales Mathematicae Silesianae, 38(1), 18–28. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/16727

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Vol. 38 No. 1 (2024)
Published: 2024-03-27

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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