Automorphisms of $\textrm {GL}_{n}(R)$
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- by Bernard R. McDonald PDF
- Trans. Amer. Math. Soc. 215 (1976), 145-159 Request permission
Abstract:
Let R be a commutative ring and S a multiplicatively closed subset of R having no zero divisors. The pair $\langle R,S\rangle$ is said to be stable if the ring of fractions of R, ${S^{ - 1}}R$, defined by S is a ring for which all finitely generated projective modules are free. For a stable pair $\langle R,S\rangle$ assume 2 is a unit in R and V is a free R-module of dimension $\geqslant 3$. This paper examines the action of a group automorphism of $GL(V)$ (the general linear group) on the elementary matrices relative to a basis B of V. In the case that R is a local ring, a Euclidean domain, a connected semilocal ring or a Dedekind domain whose quotient field is a finite extension of the rationals, we obtain a description of the action of the automorphism on all elements of $GL(V)$.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 215 (1976), 145-159
- MSC: Primary 20G35
- DOI: https://doi.org/10.1090/S0002-9947-1976-0382467-1
- MathSciNet review: 0382467