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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The closed socle of an Azumaya algebra


Author: F. R. DeMeyer
Journal: Proc. Amer. Math. Soc. 78 (1980), 299-303
MSC: Primary 16A16
MathSciNet review: 553361
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0553361-4
PII: S 0002-9939(1980)0553361-4
Article copyright: © Copyright 1980 American Mathematical Society