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Multiplicative semigroup automorphisms of upper triangular matrices over rings

โœ Scribed by Chongguang Cao; Zhang Xian

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
297 KB
Volume
278
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Suppose R is a ring with 1 and C a central subring of R. Let T,(R) be the C-algebra of upper triangular n x n matrices over R. Recently several authors have shown that if R is sufficiently well behaved, then every C-automorphism of T,,(R) is the composites of an inner automorphism and an automorphism induced from a C-automorphism of R (see [l-5]). To generalize these results. in this paper we prove that if N > 2 and R is a semiprime ring or a ring in which all idempotents are central, then f : T,,(R) 4 T,(R) (T,(R)

๐Ÿ“œ SIMILAR VOLUMES

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โœ You'an Cao ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 187 KB

Let R be an arbitrary commutative ring with identity. Denote by t the Lie algebra over R consisting of all upper triangular n by n matrices over R and let b be the Lie subalgebra of t consisting of all matrices of trace 0. The aim of this paper is to give an explicit description of the automorphism

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โœ D.Z. Dokovic ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 276 KB

Let \(R\) be a non-trivial commutative ring having no idempotents except 0 and 1 . Denote by \(t\) the Lie algebra over \(R\) consisting of all upper triangular \(n\) by \(n\) matrices over \(R\). We give an explicit description of the automorphism group of this Lie algebra. 1994 Academic Press, Inc