2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65347Given a finite--dimensional monomial algebra $A$ we consider the trivial extension $TA$ and provide formulae, depending on the characteristic of the field, for the dimensions of the summands $HH_1(A)$ and $\Alt(DA)$ of the first Hochschild cohomology group $HH^1(TA)$. From these a formula for the dimension of $HH^1(TA)$ can be derived.Final version to be published in Journal of Algebra and Its Applications (JAA). Small changes from previous version. 13 pagesK-Theory and HomologyRings and AlgebrasRepresentation Theory16E40text