2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112764Let $R$ be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial ring $R[x,f]$ (associated to $R$ and the Frobenius homomorphism $f$, in the indeterminate $x$) that is both $x$-torsion and Artinian over $R$.This is to appear in the Proceedings of the American Mathematical SocietyCommutative Algebra13A35, 13E10, 16S36 (Primary) 13D45 (Secondary)text