Roth's theorems and decomposition of modules

DOI10.1016/0024-3795(81)90300-1zbMath0468.16022OpenAlexW2094918013MaRDI QIDQ1156218

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)90300-1

zbMATH Keywords

block diagonal matricesdecomposition of modules

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Representation theory of associative rings and algebras (16Gxx)

Related Items (20)

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 ⋮ The matrix equation \(X-AXB=C\) and an analogue of Roth's theorem ⋮ Diagonalization of matrices over regular rings ⋮ 𝑝-group Galois covers of curves in characteristic 𝑝 ⋮ Similarity of matrices over local rings ⋮ The matrix linear unilateral and bilateral equations with two variables over commutative rings ⋮ Matrix equivalence and isomorphism of modules ⋮ Modules and matrices ⋮ Roth's solvability criteria for the matrix equations \(AX-\hat{X}B=C\) and \(X-A\hat{X}B=C\) over the skew field of quaternions with an involutive automorphism \(q \mapsto \hat{q}\) ⋮ 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 ⋮ On decomposing any matrix as a linear combination of three idempotents ⋮ The generalized inverse of a sum with radical element: Applications ⋮ The direct extension theorem ⋮ The direct product theorem for profinite groups ⋮ A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity ⋮ Roth's removal rule revisited ⋮ Algebraic conditions for the solvability to some systems of matrix equations ⋮ Roth's theorems for sets of matrices

Cites Work

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• On matrix equivalence and matrix equations
• 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
• Roth's Equivalence Problem in Unit Regular Rings
• The Equations AX - YB = C and AX - XB = C in Matrices

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