Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1980-0553361-4
MathSciNet review: 553361
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A16

Retrieve articles in all journals with MSC: 16A16


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0553361-4
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society