2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67627In [Kat94b], Kato defined his notion of a log regular scheme and studied the local behavior of such schemes. A toric variety equipped with its canonical logarithmic structure is log regular. And, these schemes allow one to generalize toric geometry to a theory that does not require a base field. This paper will extend this theory by removing normality requirements.new longer introduction, other minor improvements, 35 pagesCommutative AlgebraAlgebraic Geometry14M25 (primary); 20M25 (secondary)text