Derivations on algebras of one-point compactification of affine semigroups
Roberto D\'iaz

TL;DR
This paper investigates derivations on the semigroup algebra of the one-point compactification of affine semigroups, linking their structure to derivations on the original semigroup algebra within a metrizable topology.
Contribution
It provides a detailed analysis of derivations on the algebra of the one-point compactification of affine semigroups, extending understanding of their algebraic and topological properties.
Findings
Characterization of derivations on the compactified semigroup algebra
Relation between derivations on the compactified and original semigroup algebras
Insights into the topology-induced structure of derivations
Abstract
For any affine semigroup the set has a natural structure of semigroup, additionally if is endowed with the discrete topology, the semigroup can be studied as the one-point compactification of . In this article we study the derivations on the semigroup algebra in relation to the derivations on the semigroup algebra considering the metrizable topology on induced by the one-point compactification topology of .
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