[For the entire collection see Zbl 0537.00005.]
Let \(k\) be a commutative ring, \(H\) a Hopf algebra over \(k\) which is finitely- generated projective as \(k\)-module. Let \(R\) be an \(H\)-module algebra and \(R{\#}H\) the smash product. For the dual Hopf algebra \(H^*\), \(R{\#}H\) is an \(H^*\)-module algebra, so we can form \((R{\#}H){\#}H^*\). Montgomery and Blattner have shown that \((R{\#}H){\#}H^*\) is isomorphic (as \(k\)-algebra) to \(\text{End}_ R(R\#H)\), where \(R{\#}H\) is considered as right \(R\)-module via \(R\to R\#H\). In this note, the author gives another proof using non-commutative Galois theory.