Matrix equivalence and isomorphism of modules

DOI10.1016/0024-3795(82)90248-8zbMath0493.16015OpenAlexW2077315712MaRDI QIDQ1168401

Robert M. Guralnick

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0024-3795(82)90248-8

zbMATH Keywords

block matricesstable rangeequivalent matricessimilar matricesdecomposition of modules

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Free, projective, and flat modules and ideals in associative algebras (16D40) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Representation theory of associative rings and algebras (16Gxx)

Related Items (13)

A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications ⋮ The extension of Roth's theorem for matrix equations over a ring ⋮ Homomorphisms of progenerator modules under a change of base ring ⋮ Modules and matrices ⋮ Local to global equivalence for homomorphisms ⋮ Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra ⋮ An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications ⋮ Exchange rings with stable range one ⋮ Invariant factors of an endomorphism and finite free resolutions ⋮ ON THE WEAK GROTHENDIECK GROUP OF A BEZOUT RING ⋮ A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity ⋮ Elementary Divisor Theorem for Noncommutative Pids ⋮ Roth's theorems for sets of matrices

Cites Work

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• On matrix equivalence and matrix equations
• Roth's theorems and decomposition of modules
• Module equivalences: Local to global. When primitive polynomials represent units
• Algebras over zero-dimensional rings
• Roth's theorems over commutative rings
• Matrices and pairs of modules
• Note on direct summands of modules
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Equivalence of partitioned matrices
• Roth's Equivalence Problem in Unit Regular Rings
• Stable equivalence of matrices and resolutions
• Some Ring Theoretic Schroder-Bernstein Theorems
• Maximal Orders
• The Equations AX - YB = C and AX - XB = C in Matrices
• Algebraic \(K\)-theory

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