Determinants of Galois automorphisms of maximal commutative rings of \(2\times 2\) matrices

DOI10.1016/0024-3795(79)90045-4zbMath0418.15011OpenAlexW1963548697MaRDI QIDQ755635

Dennis R. Estes

Publication date: 1979

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(79)90045-4

zbMATH Keywords

Galois cohomologyPicard groupmatrix equations

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (2)

Composition of binary integral quadratic forms via integral 2 × 2 matrices and composition of matrix classes ⋮ Representations under ring extensions: Latimer-MacDuffee and Taussky correspondences

Cites Work

• On matrix classes corresponding to an ideal and its inverse
• Additive commutators of rational \(2\times 2\) matrices
• Norms in quadratic fields and their relations to non commuting \(2\times 2\) matrices. I
• Norms from quadratic fields and their relation to noncommuting \(2\times 2\) matrices. III: A link between the 4-rank of ideal class groups in \(Q(\sqrt m)\) and in \(Q(\sqrt{-m})\).
• Separable algebras over commutative rings
• The role of symmetric matrices in the study of general matrices
• Ideal matrices. I
• Matrices of rational integers
• Additive commutators between 2×2 integral matrix representations of orders in identical or different quadratic number fields
• The factorization of an integral matrix into a product of two integral symmetric matrices
• The factorization of an integral matrix into a product of two integral symmetric matrices, II. The general case n=2
• The factorization of an integral matrix into a product of two integral symmetric matrices I
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