%0 Journal Article %T On the Hartshorne--Speiser--Lyubeznik Theorem about Artinian modules with a Frobenius action %A Rodney Y. Sharp %J Mathematics %D 2006 %I arXiv %X Let $R$ 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 $R$. %U http://arxiv.org/abs/math/0605330v1