Automorphisms of $\textrm {GL}_{n}(R)$
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 by B. R. McDonald PDF
 Trans. Amer. Math. Soc. 246 (1978), 155171 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 βstableβ 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

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Additional Information
 © Copyright 1978 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 246 (1978), 155171
 MSC: Primary 20G99
 DOI: https://doi.org/10.1090/S00029947197805155341
 MathSciNet review: 515534