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 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]**Maurice Auslander and Oscar Goldman,*The Brauer group of a commutative ring*, Trans. Amer. Math. Soc.**97**(1960), 367–409. MR**0121392**, 10.1090/S0002-9947-1960-0121392-6**[2]**Charles W. Curtis and Irving Reiner,*Representation theory of finite groups and associative algebras*, Pure and Applied Mathematics, Vol. XI, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962. MR**0144979****[3]**F. R. DeMeyer,*Projective modules over central separable algebras*, Canad. J. Math.**21**(1969), 39–43. MR**0234987****[4]**Frank DeMeyer and Edward Ingraham,*Separable algebras over commutative rings*, Lecture Notes in Mathematics, Vol. 181, Springer-Verlag, Berlin-New York, 1971. MR**0280479****[5]**F. R. Demeyer and M. A. Knus,*The Brauer group of a real curve*, Proc. Amer. Math. Soc.**57**(1976), no. 2, 227–232. MR**0412193**, 10.1090/S0002-9939-1976-0412193-7**[6]**Darrell E. Haile,*The closed socle of a central separable algebra*, J. Algebra**51**(1978), no. 1, 97–106. MR**0463225**

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

Article copyright:
© Copyright 1980
American Mathematical Society