%0 Journal Article %T A note on smoothness and differential bases in positive characteristic %A Cristodor Ionescu %J Mathematics %D 2008 %I arXiv %X Let $u:A\to B$ be a morphism of noetherian local rings. We obtain smoothness criteria for algebras with differential bases, in the case of rings containing a field of characteristic $p>0.$ We also give smoothness criteria for reduced morphisms. %U http://arxiv.org/abs/0809.4559v2