Linear groups over general rings. I: Generalities. (Q354787)

scientific article; zbMATH DE number 6189849

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English	Linear groups over general rings. I: Generalities.	scientific article; zbMATH DE number 6189849

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instance of

scholarly article

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title

Linear groups over general rings. I: Generalities. (English)

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published in

Journal of Mathematical Sciences (New York)

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publication date

22 July 2013

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review text

This paper is the first part of a systematic survey on the structure of classical groups over general rings. It covers background material such as one-sided inverses, elementary transformations, definitions of obvious subgroups, Bruhat and Gauss decompositions, relative subgroups, finitary phenomena, and transvections.

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zbMATH Keywords

classical groups over rings

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general linear groups

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groups of matrices

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survey

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full work available at URL

https://doi.org/10.1007/s10958-013-1146-7

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Normal Subgroups of Orthogonal Groups Over Commutative Rings

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Reduction of a Matrix Depending on Parameters to a Diagonal Form by Addition Operations

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Q3831197

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Normal subgroups of symplectic groups over rings

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Q3822313

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The subnormal structure of general linear groups over rings

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Q3473287

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On the Whitehead determinant for semi-local rings

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Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups

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Prestabilization for $K_ 1$ of Banach algebras

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Q3485004

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Commutators and companion matrices over rings of stable rank 1

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Normal subgroups of classical groups over rings

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A note on the subnormal structure of general linear groups

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Q4271238

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Q4867070

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A third look at weight diagrams

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ON POSITIVE THEORIES OF GROUPS WITH REGULAR FREE LENGTH FUNCTIONS

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Chevalley groups over commutative rings. I: Elementary calculations

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Projective planes over rings of stable rank 2

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Spherical posets and homology stability for $O_ n,$//n

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The general linear group of polynomial rings over regular rings

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On K 2 of the Laurent Polynomial Ring

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Stability for homology of the general linear group of a local ring

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G$L_ 2$ over full rings

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Q3691936

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Defining relations for certain integrally parametrized Chevalley groups

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Q3884236

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Automorphisms of GL n (R)

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Automorphisms of quotients of PiGL(n//i)

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Automorphisms of $\det (X_{ij}):$ The group scheme approach

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On abstract homomorphisms of anisotropic algebraic groups over real-closed fields

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Monomorphisms between subgroups of groups of type $G_ 2$.

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Abstract isomorphisms of simple algebraic groups split by quadratic extensions

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Q3682604

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Q3540964

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1-Homotopy of Chevalley Groups

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On nilpotent class 2 groups and the Steinberg groups ST(3,R)

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Q5647103

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Products of similar matrices

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The amalgamated free product structure of 𝐺𝐿₂(𝐾[𝑋₁,⋯,𝑋_{𝑛}])

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The amalgamated free product structure of $\mathrm{GL}_2(k[X_1,\dots ,X_n ])$ and the weak Jacobian theorem for two variables

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On the Homology of GLnand Higher Pre-Bloch Groups

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Triangular and diagonal forms for matrices over commutative noetherian rings

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Prestabilization for $K_ 1U^ \varepsilon$ of $\Lambda$-2-fold rings

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Stabilization of unitary groups over polynomial rings

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Subrings in Quadratic Fields Which are Not Universal for GE2

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Prestability for quadratic $K_1$ of $\Lambda$-1-fold stable rings

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The Quillen - Suslin theorem and the structure of n-dimensional elementary polynomial matrices

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An embedding theorem between special linear groups over any fields

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On weak resolutions

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Determination of Homomorphisms between Linear Groups of the same Degree over Division Rings

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Q3743500

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Stable sandwich classification theorem for classical-like groups

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Subnormal structure of non-stable unitary groups over rings.

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Q3695473

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Zur $\mathrm{SL}_2$ der ganzen Zahlen eines imaginär-quadratischen Zahlkörpers

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Identifiers

zbMATH Open document ID

1278.20066

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Mathematics Subject Classification ID

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10.1007/S10958-013-1146-7

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Sitelinks

Mathematics(1 entry)

mardi Publication:354787