Matrices and pairs of modules

DOI10.1016/0021-8693(74)90079-9zbMath0282.16001OpenAlexW2027017242MaRDI QIDQ1843476

J. Chris Robson, Lawrence S. Levy

Publication date: 1974

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(74)90079-9

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Divisibility, noncommutative UFDs (16U30) Representation theory of associative rings and algebras (16Gxx)

Related Items (27)

Wild torsion modules over Weyl algebras and general torsion modules over HNPs ⋮ Auslander–Bridger Modules ⋮ Reduction of matrices over simple Ore domains ⋮ Green’s relation ℋ on the monoid of square matrices over a specific local ring ⋮ The number of generators of a module over a fully bounded ring ⋮ Roth's theorems and decomposition of modules ⋮ Power equivalence of presentations ⋮ Matrix equivalence and isomorphism of modules ⋮ Local to global equivalence for homomorphisms ⋮ Equivalence of diagonal matrices over local rings. ⋮ On graded Cartan invariants of symmetric groups and Hecke algebras ⋮ Decomposing a projective module and several submodules ⋮ Generalized commutators in matrix rings ⋮ A local approach to matrix equivalence ⋮ Stable equivalence of matrices and resolutions ⋮ Left comorphic matrix rings ⋮ Block diagonalization and $2$-unit sums of matrices over Prüfer domains ⋮ Sometimes Only Square Matrices can be Diagonalized ⋮ Equivalence of von Neumann regular and idempotent matrices ⋮ Presentations over HNP rings with enough invertible ideals and torsionfree cancellation over neoclassical orders ⋮ FFRT properties of hypersurfaces and their F-signatures ⋮ The genus of a module ⋮ A note on matrix inversion ⋮ Elementary Divisor Theorem for Noncommutative Pids ⋮ Hereditary Noetherian prime rings. II: Finitely generated projective modules ⋮ Modules over prime Krull rings ⋮ On local orders

Cites Work

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• Non-commutative principal ideal rings
• On the sources of my book \textit{Moderne Algebra}
• Non-commutative Dedekind rings
• Left principal ideal rings
• Modules over Dedekind prime rings
• Hereditary Noetherian prime rings
• Ideals and modules of simple Noetherian hereditary rings
• Almost diagonal matrices over Dedekind domains
• Homomorphisms and extensions of modules over certain differential polynomial rings
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Non-commutative domains of integrity.
• Decomposing Pairs of Modules
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• A survey of integral representation theory
• A Note on Dedekind Prime Rings
• Completions of Non-Commutative Dedekind Prime Rings
• Elementary Divisors and Modules

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