Isomorphisms of a complete linear group over an associative ring

zbMath0534.20033MaRDI QIDQ790258

Alexander V. Mikhalev, Igor Z. Golubchik

Publication date: 1983

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

zbMATH Keywords

elementary matricescentral idempotentsmatrix ringsautomorphism of complete linear groupstandard isomorphism

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Automorphisms of infinite groups (20E36) Other matrix groups over rings (20H25)

Related Items (27)

Elementary equivalence of unitary linear groups over rings. ⋮ Combinatorial and logical aspects of linear groups and Chevalley groups. ⋮ Linear groups over general rings. I: Generalities. ⋮ Automorphisms and isomorphisms of Chevalley groups and algebras. ⋮ Isomorphisms of the linear groups \(\operatorname{GL}_{2}(R)\) over associative rings \(R\) ⋮ Automorphisms of elementary adjoint Chevalley groups of types \(A_l\), \(D_l\), and \(E_l\) over local rings with \(1/2\). ⋮ Elementary equivalence of categories of modules and other algebraic structures. ⋮ Elementary equivalence of stable linear groups over local commutative rings with \(1/2\) ⋮ Isomorphisms of general linear groups over associative rings graded by an Abelian group. ⋮ Endomorphism rings of modules and lattices of submodules ⋮ Automorphisms of Chevalley groups of type \(F_4\) over local rings with \(1/2\). ⋮ Stable groups over associative rings with \(1/2\). A description of isomorphisms of the stable linear groups. ⋮ Elementary equivalence of linear groups over rings with a finite number of central idempotents and over Boolean rings. ⋮ Automorphisms of Chevalley groups of type \(B_l\) over local rings with \(1/2\). ⋮ Automorphisms of Chevalley groups of types \(A_l\), \(D_l\), \(E_l\) over local rings without \(1/2\). ⋮ Isomorphisms of stable linear groups over associative rings containing \(\frac{1}{2}\). ⋮ Automorphisms of Chevalley groups of different types over commutative rings. ⋮ Homomorphisms of two-dimensional linear groups over a ring of stable range one. ⋮ The radical \(RN\) and the weakly solvable radical of linear groups over associative rings. ⋮ Automorphisms of Chevalley groups of types \(B_2\) and \(G_2\) over local rings. ⋮ Automorphisms of stable linear groups over commutative local rings with \(1/2\). ⋮ Universal equivalence of linear groups over local commutative rings with \(1/2\) ⋮ Chevalley groups over commutative rings. I: Elementary calculations ⋮ Definability of completely decomposable torsion-free abelian groups by endomorphism semigroups and homomorphism groups ⋮ Homomorphisms of linear groups over rings ⋮ Isomorphisms of unitary groups over associative rings ⋮ Isomorphisms of general linear groups over rings

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