Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Inertial subalgebras of central separable algebras
HTML articles powered by AMS MathViewer

by Nicholas S. Ford PDF
Proc. Amer. Math. Soc. 60 (1976), 39-44 Request permission


Let R be a commutative ring with 1. An R-separable subalgebra B of an R-algebra A is said to be an R-inertial subalgebra provided $B + N = A$, where N is the Jacobson radical of A. Suppose A is a finitely generated R-algebra which is separable over its center $Z(A)$. We show that if A possesses an R-inertial subalgebra B, then $Z(A)$ possesses a unique Rinertial subalgebra S. Moreover, A can be decomposed as $A \simeq B{ \otimes _S}Z(A)$. Suppose C is a finitely generated, commutative, semilocal R-algebra with Rinertial subalgebra S. We show that the R-inertial subalgebras of each central separable C-algebra are unique up to an inner automorphism generated by an element in the radical of the algebra if and only if the natural mapping of the Brauer groups $\beta (S) \to \beta (C)$ is a monomorphism. We conclude by presenting a method which enables one to construct algebras which possess nonisomorphic inertial subalgebras.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A16
  • Retrieve articles in all journals with MSC: 16A16
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 39-44
  • MSC: Primary 16A16
  • DOI:
  • MathSciNet review: 0414607