Diagonalization of matrices over regular rings

DOI10.1016/S0024-3795(96)00596-4zbMath0883.15006MaRDI QIDQ1369352

K. C. O'Meara, Kenneth R. Goodearl, Enrique Pardo Espino, Pere Ara

Publication date: 22 March 1998

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

zbMATH Keywords

projective modulesdiagonalizationexchange ringsvon Neumann regular ringssquare matrixregular matrices

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Canonical forms, reductions, classification (15A21)

Related Items (36)

Power-substitution,exchange rings and unit II-regularity ⋮ On Uniform Diagonalisation of Matrices over Regular Rings and One-Accessible Regular Algebras ⋮ RIGHT SELF-INJECTIVE RINGS IN WHICH EVERY ELEMENT IS A SUM OF TWO UNITS ⋮ Related comparability over exchange rings ⋮ On ExchangeQB-Rings ⋮ Reduction of matrices over simple Ore domains ⋮ EXCHANGE RINGS OVER WHICH EVERY REGULAR MATRIX ADMITS DIAGONAL REDUCTION ⋮ On Hermitian endomorphism rings ⋮ The Moore-Penrose inverse of a factorization ⋮ Additive Representations of Elements in Rings: A Survey ⋮ Generalized Stable Exchange Rings ⋮ On Exchange QB_∞-Rings ⋮ On products of three triangular matrices over associative rings ⋮ REGULAR RINGS WITH FINITE STABLE RANGE ⋮ On strongly \(\pi\)-regular ideals. ⋮ A stable range of class full matrices over elementary divisor ring ⋮ DECOMPOSING ELEMENTS OF A RIGHT SELF-INJECTIVE RING ⋮ SUMS OF UNITS IN RINGS ⋮ On similarity of matrices over commutative rings ⋮ The Moore-Penrose inverse of von Neumann regular matrices over a ring ⋮ Diagonal reductions of matrices over exchange ideals ⋮ On Generalized Stable Ideals ⋮ Generalized commutators in matrix rings ⋮ Generalized Stable Regular Rings ⋮ Generalized Ideal-Stable Regular Rings ⋮ On generalized stable rings ⋮ Strong separativity over exchange rings ⋮ Separative cancellation for projective modules over exchange rings ⋮ On rings with associated elements ⋮ OnQB_∞-Rings ⋮ Regular morphisms in abelian categories ⋮ Separative Cancellation over Regular Rings ⋮ On Exchange Hermitian Rings ⋮ Extensions of Exchange QB-Rings ⋮ Modules invariant under automorphisms of their covers and envelopes. ⋮ Exchange rings having ideal-stable range one

Cites Work

• Unnamed Item
• On rings whose projective modules have the exchange property
• Aleph-nought-continuous regular rings
• Roth's theorems and decomposition of modules
• On regular rings with stable range 2
• Separative cancellation for projective modules over exchange rings
• The pyramid decomposition and rank minimization
• Embedding simple commutative monoids into simple refinement monoids
• Completion of diagrams by automorphisms and Bass' first stable range condition
• Refinements for infinite direct decompositions of algebraic systems
• Exchange rings and decompositions of modules
• On a class of regular rings that are elementary divisor rings
• Rational \(C^*\)-algebras and nonstable K-theory
• Pseudo-similarity and partial unit regularity
• Sometimes Only Square Matrices can be Diagonalized
• Roth's Equivalence Problem in Unit Regular Rings
• On power cancellative Archimedian semigroups
• Elementary Divisors and Modules

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