Automorphisms of upper triangular matrix rings

Jøndrup, S.

doi:10.1007/bf01194296

Cited by 37 publications

(12 citation statements)

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“…In [1] automorphisms of the ring of triangular endomorphisms of countable dimensional linear spaces were described. Jondrup [133] proved for a simple Artinian ring A, finite dimensional over its center F, that every F-automorphism of T n (A), the ring of triangular (n x n)-matrices over A, is inner.…”

Section: Isomorphisms and Automorphisms Of Triangular And Structural mentioning

confidence: 99%

Isomorphisms and anti-isomorphisms of endomorphism rings of modules

Mikhalev¹

1996

First International Tainan-Moscow Algebra Workshop

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Let A and B be rings and Ma and Ng a right A-module and a right 5-module respectively. Let a:End(M,4) -»• End(Ar fl ) be either an isomorphism or an anti-isomorphism of their endomorphism rings. The Wedderburn-Baer-Kaplansky problem is to characterize all such a. The problem has a long history. The aim of these lectures is to consider main results in this direction for modules Ma and Ng which are close to free ones (in the epicenter we put strong generators, i.e., modules with a cyclic free direct summand). The problems under consideration are connected with conditions for inducing of isomorphisms of endomorphism rings by semilinear transformations, by Morita equivalences or by full embeddings. We consider also multiplicative isomorphisms of endomorphism semigroups of modules. We touch some related topics. First of all, we describe recent results on isomorphisms of general linear groups over arbitrary associative rings (Schreier -van der Waerden problem), because of a nice reduction of this group problem to the ring problem of classification of isomorphisms and anti-isomorphisms of matrix rings. We consider Malcev type theorems on elementary equivalences of linear groups and rings of matrices. At the same time we deal with the characterization problem of endomorphism rings of modules from different classes (in particular, of matrix rings). Some comments are related to operator rings and semigroups of topological and ordered linear spaces and to Frobenius type results on A-linear mappings on matrix rings A n .

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Section: Isomorphisms and Automorphisms Of Triangular And Structural mentioning

confidence: 99%

Isomorphisms and anti-isomorphisms of endomorphism rings of modules

Mikhalev¹

1996

First International Tainan-Moscow Algebra Workshop

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“…To determine the automorphisms of classical Lie algebras over commutative rings was recently studied in [1][2][3][4][5][6][7]. In this article, based on the main theorem in [2], we give an explicit description of the automorphisms of the standard Borel subalgebra l of sp(2m, R), provided that R is a commutative ring with identity, 2 is invertible in R.…”

Section: Introductionmentioning

confidence: 98%

Automorphisms of the standard Borel subalgebra of Lie algebra ofC_mtype over a commutative ring

Wang

2007

Linear and Multilinear Algebra

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“…A lot of work has been done in studying automorphisms and derivations of matrix algebras and their subalgebras [1,2,5,[8][9][10]12], and those of general linear Lie algebras and their subalgebras [13,15,16]. Li and Wang [11] characterized the generalized Lie triple derivations of a Borel subalgebra (or its derivation algebra) of a complex simple Lie algebras.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear maps satisfying derivability on the parabolic subalgebras of the general linear Lie algebras

Chen

Wang

2012

Linear and Multilinear Algebra

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Automorphisms of upper triangular matrix rings

Cited by 37 publications

References 1 publication

Isomorphisms and anti-isomorphisms of endomorphism rings of modules

Isomorphisms and anti-isomorphisms of endomorphism rings of modules

Automorphisms of the standard Borel subalgebra of Lie algebra ofC_mtype over a commutative ring

Nonlinear maps satisfying derivability on the parabolic subalgebras of the general linear Lie algebras

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Automorphisms of upper triangular matrix rings

Cited by 37 publications

References 1 publication

Isomorphisms and anti-isomorphisms of endomorphism rings of modules

Isomorphisms and anti-isomorphisms of endomorphism rings of modules

Automorphisms of the standard Borel subalgebra of Lie algebra ofCmtype over a commutative ring

Nonlinear maps satisfying derivability on the parabolic subalgebras of the general linear Lie algebras

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Product

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Automorphisms of the standard Borel subalgebra of Lie algebra ofC_mtype over a commutative ring