quaternion algebras contain quadratic field extensions of the center. given two algebras, a natural question to ask is whether they share a common field extension. this gives us an idea of how closely related those algebras are to one another. if the center is of characteristic 2 then those extensions divide into two types - the separable type and the inseparable type. it is known that if two quaternion algebras share an inseparable field extension then they also share a separable field extension and that the converse is not true. we shall discuss this fact and its generalization to p-algebras of arbitrary prime degree.