2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66853We develop a theory of G-dimension for modules over local homomorphisms which encompasses the classical theory of G-dimension for finite modules over local rings. As an application, we prove that a local ring R of characteristic p is Gorenstein if and only if it possesses a nonzero finite module of finite projective dimension that has finite G-dimension when considered as an R-module via some power of the Frobenius endomorphism of R. We also prove results that track the behavior of Gorenstein properties of local homomorphisms under (de)composition.31 pages, uses Xy-picCommutative AlgebraAlgebraic Geometry13D05, 13D25, 13B10, 13H10, 14B25text