Extensões de Hopf-Ore e a décima conjectura de Kaplansky

Abstract

In this work we will treat, in particular, of the Hopf algebras and Hopf-Ore extensions. One of ours main goals is to prove a theorem that characterizes when a Hopf algebra R is a extension of Hopf-Ore of a Hopf algebra H. This theorem has been proved by A. N. Panov in (PANOV, 2003). Furthermore, we use iterated extensions of Hopf-Ore to build Hopf algebras pointed and co-Frobenius and with that give a negative answer to the tenth Kaplansky’s conjecture.