The purpose of this paper is to complete the classification of almost involutive Hopf algebras up to dimension 23. For this, we first present a brief survey of these algebras, showing that most of them can be obtained by iterated Hopf-Ore extensions. Then the classification follows using a technique we developed for determining when a Hopf-Ore extension is almost involutive.

We develop a partial Hopf-Galois theory for partial Hmodule algebras and we recover analogs of classical results for Hopf algebras.

Resumo Desenvolver um conhecimento sólido sobre as equações diofantinas lineares em duas variáveis possibilita a resolução de muitos problemas do cotidiano e, também, o real entendimento de alguns conceitos matemáticos