<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <italic>S</italic> of a group <italic>G</italic> generates <italic>G</italic> in the sense that <italic>G</italic> = <italic>S · S</italic><sup>−1</sup>, then a generalized polynomial on <italic>S</italic> with values in an Abelian group <italic>H</italic> can be extended to a generalized polynomial on <italic>G</italic> into <italic>H</italic>. Finally there is a short discussion of the extendability of exponential functions and generalized exponential polynomials.</p>
</abstract>

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.

Generalized Polynomials on Semigroups

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

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...

Generalized Polynomials on Semigroups

Published Online: Jan 10, 2024

Page range: 18 - 28

Received: Jul 19, 2023

Accepted: Dec 11, 2023

DOI: https://doi.org/10.2478/amsil-2023-0026

Keywords
homomorphism, semigroup, multi-homomorphism, multi-additive function, generalized polynomial, extension

© 2023 Bruce Ebanks, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Generalized Polynomials on Semigroups

Published Online: Jan 10, 2024

Page range: 18 - 28

Received: Jul 19, 2023

Accepted: Dec 11, 2023

DOI: https://doi.org/10.2478/amsil-2023-0026

Keywordshomomorphism, semigroup, multi-homomorphism, multi-additive function, generalized polynomial, extension

© 2023 Bruce Ebanks, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
homomorphism, semigroup, multi-homomorphism, multi-additive function, generalized polynomial, extension