ON SEPARABLE SUBALGEBRAS OF AZUMAYA ALGEBRAS

George Szeto
1998 MATEMATIQKI VESNIK   unpublished
Let A be an Azumaya C-algebra. Then the set of all commutative separable subalgebras of A and the set of separable subalgebras B such that VA(B) = VB(B) are in a one-to-one correspondence, where VA(B) is the commutator subring of B in A, and the set of all separable subalgebras of A is a disjoint union of the Azumaya algebras in A over a commutative separable subalgebra of A. The results are used to compute splitting rings for an Azumaya s k ew group ring.
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