Similarity of matrices over local rings

DOI10.1016/0024-3795(81)90096-3zbMath0478.15017OpenAlexW1982915964MaRDI QIDQ1160692

Robert M. Guralnick

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1016/0024-3795(81)90096-3

zbMATH Keywords

similaritylocal ringmatrices of analytic functions

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrices over function rings in one or more variables (15A54)

Related Items

Two-generated commutative matrix subalgebras ⋮ Similarity of holomorphic matrices ⋮ Matrix zeros of quadratic equations ⋮ Similarity classes for nilpotent operators over Dedekind domains ⋮ Polynomial equations for matrices over integers modulo a prime power and the cokernel of a random matrix ⋮ On similarities of class \(C^ p\) and applications to matrix differential equations ⋮ Modules and matrices ⋮ Similarity of matrices over commutative rings ⋮ Normal forms of holomorphic matrix-valued functions and corresponding forms for singular differential operators ⋮ Rosenbrock's theorem for systems over von Neumann regular rings ⋮ Local to global equivalence for homomorphisms ⋮ Globally analytic triangularization of a matrix function ⋮ Block conjugacy of irreducible toral automorphisms ⋮ Roth's removal rule revisited ⋮ The pointwise-local-global principle for solutions of generic linear equations

Cites Work

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• On holomorphically similar matrices
• On pointwise and analytic similarity of matrices
• A note on the local-global principle for similarity of matrices
• Roth's theorems and decomposition of modules
• Similarity of matrices over Artinian principal ideal rings
• Roth's theorems over commutative rings
• Matrices similar on a Zariski-open set
• Invariant Factors and Two Criteria for Projectivity of Modules
• Modules over commutative regular rings