The closed socle of an Azumaya algebra

Author:
F. R. DeMeyer

Journal:
Proc. Amer. Math. Soc. **78** (1980), 299-303

MSC:
Primary 16A16

DOI:
https://doi.org/10.1090/S0002-9939-1980-0553361-4

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 in *R*, called the closed socle of *A*, is defined and it is shown that is independent of the representative *A* in the Brauer group of *R*. When *R* is a domain, the behavior of under localization and passage to the quotient field is studied, and is calculated when *R* is the affine ring of a real curve.

**[1]**M. Auslander and O. Goldman,*The Brauer group of a commutative ring*, Trans. Amer. Math. Soc.**97**(1960), 367-409. MR**0121392 (22:12130)****[2]**C. W. Curtis and I. Reiner,*Representation theory of finite groups and associative algebras*, Interscience, New York, 1962. MR**0144979 (26:2519)****[3]**F. R. DeMeyer,*Projective modules over central separable algebras*, Canad. J. Math.**21**(1969), 39-43. MR**0234987 (38:3299)****[4]**F. R. DeMeyer and E. Ingraham,*Separable algebras over commutative rings*, Lecture Notes in Math., vol. 181, Springer-Verlag, Berlin and New York, 1971. MR**0280479 (43:6199)****[5]**F. R. DeMeyer and M. A. Knus,*The Brauer group of a real curve*, Proc. Amer. Math. Soc.**58**(1976), 227-232. MR**0412193 (54:320)****[6]**D. Haile,*The closed socle of a central separable algebra*, J. Algebra**51**(1978), 97-106. MR**0463225 (57:3181)**

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0553361-4

Article copyright:
© Copyright 1980
American Mathematical Society