On bicommutators of modules over \(H\)-separable extension rings. II (Q1185416)

This paper (and this review) is a continuation of part I [see the preceding review Zbl 0749.16018]. Previous results on bicommutators are applied when \(A\) is an Azumaya \(R\)-algebra, \(R\) commutative, a special case of an \(H\)-separable extension. For example, then, \(R^*\) is commutative, \(A^*\) is an Azumaya \(R^*\)-algebra, and for any separable \(R\)-subalgebra \(B\) of \(A\), \(B^*\) is a separable \(R^*\)-subalgebra of \(A\). Also if \(_ AM\) and \(_ AN\) are weakly isomorphic (each weakly divides the other), then \(\text{Bic}(_ AM)\cong \text{Bic}(_ AN)\). The final section of this paper applies previous results to strongly primitive rings.