| This thesis studies equivalence classes of G-algebras over connected rings, where G is a finite group. Equivalence classes of central simple G-algebras over fields was introduced and later invariants of the classes were formulated by Turull in [9] and [12]. The set of equivalence classes of interior central simple G-algebras over a field F was shown to be isomorphic to the direct product of H2(G, K*) x Br(F) by Herman in [15].;The goal of this thesis is to define equivalence classes of G-algebras over commutative rings. Such equivalence classes can be defined over general rings. When the base ring is a PID the results are similar to those for the interior central simple G-algebras over a field. When the base ring is connected but not a PID, a full set of invariants are defined of the equivalence classes of the G-algebras. The main theorem, Theorem 4.2.11, proves that the equivalence class of a G-algebra is completely determined by its Brauer class and the centroid. |
