The closed socle of an Azumaya algebra

DeMeyer, F. R.

doi:10.1090/S0002-9939-1980-0553361-4

The closed socle of an Azumaya algebra
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Proc. Amer. Math. Soc. 78 (1980), 299-303 Request permission

Abstract:

If R is a Noetherian ring and A is an Azumaya algebra over R then an ideal $H(A)$ in R, called the closed socle of A, is defined and it is shown that $H(A)$ is independent of the representative A in the Brauer group of R. When R is a domain, the behavior of $H(A)$ under localization and passage to the quotient field is studied, and $H(A)$ is calculated when R is the affine ring of a real curve.

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