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Some Levi-Civita Functional Equations on Semigroups

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Abstract

The theory developed for solving Levi–Civita functional equations is more comprehensive on groups than it is on semigroups, due to the existence of prime ideals in semigroups. Here we solve on semigroups a particular Levi–Civita equation of importance to the theory, and we use that result together with representation theory to solve the general Levi–Civita equation with three summands on commutative monoids. The results also give the continuous solutions on topological semigroups and monoids.

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The author declares that no funds, grants, or other support were received during the preparation of this manuscript.

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  1. Department of Mathematics and Statistics, Mississippi State University, Starkville, MS, 39762, USA

    Bruce Ebanks

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  1. Bruce Ebanks
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Correspondence to Bruce Ebanks.

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Ebanks, B. Some Levi-Civita Functional Equations on Semigroups. Results Math 77, 154 (2022). https://doi.org/10.1007/s00025-022-01705-5

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  • DOI: https://doi.org/10.1007/s00025-022-01705-5

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