Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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.

 

Automorphisms of $\textrm {GL}_{n}(R)$
HTML articles powered by AMS MathViewer

by B. R. McDonald PDF
Trans. Amer. Math. Soc. 246 (1978), 155-171 Request permission

Abstract:

Let R denote a commutative ring having 2 a unit. Let ${\text {G}}{{\text {L}}_n}\left ( R \right )$ denote the general linear group of all $n \times n$ invertible matrices over R. Let $\wedge$ be an automorphism of ${\text {G}}{{\text {L}}_n}\left ( R \right )$. An automorphism $\wedge$ is β€œstable” if it behaves properly relative to families of commuting involutions (see Β§IV). We show that if R is connected, i.e., 0 and 1 are only idempotents, then all automorphisms $\wedge$ are stable. Further, if $n \geqslant 3$, R is an arbitrary commutative ring with 2 a unit, and $\wedge$ is a stable automorphism, then we obtain a description of $\wedge$ as a composition of standard automorphisms.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 20G99
  • Retrieve articles in all journals with MSC: 20G99
Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 246 (1978), 155-171
  • MSC: Primary 20G99
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0515534-1
  • MathSciNet review: 515534