Conjugates of an algebraic element

Let \(L/K\) be a field extension and let \(\alpha\in L\) be algebraic over \(K\), with minimal polynomial \(m_\alpha\in K[x]\), the monic irreducible polynomial in \(K[x]\) having \(\alpha\) as a root. A conjugate of \(\alpha\) over \(K\) is a root of \(m_\alpha\), in a splitting field of \(m_\alpha\) over \(L\), other than \(\alpha\).