Linear equations over commutative rings and determinantal ideals

DOI10.1016/0021-8693(86)90054-2zbMath0588.13002OpenAlexW2003086573MaRDI QIDQ1073098

J. A. Hermida, Tomás Sánchez-Giralda

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0021-8693(86)90054-2

zbMATH Keywords

determinantPrüfer ringsolution of system of linear equations over commutative ring

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Equations in general fields (12E12) Linear equations (linear algebraic aspects) (15A06) General commutative ring theory (13A99)

Related Items (13)

Commutators of trace zero matrices over principal ideal rings ⋮ Bounded reduction of orthogonal matrices over polynomial rings ⋮ Bounded reduction for Chevalley groups of types \(E_6\) and \(E_7\) ⋮ A characterization of Prüfer \(v\)-multiplication domains in terms of linear equations ⋮ Linear equations over commutative rings and grade theory ⋮ Strong surjectivity of mappings of some 3-complexes into \(M_{Q_8}\) ⋮ Hidden constructions in abstract algebra. VI: The theorem of Maroscia and Brewer {\&} Costa ⋮ Assignable polynomials to linear systems over von Neumann regular rings ⋮ Equivalent generating pairs of an ideal of a commutative ring ⋮ Equivalent generating vectors of finitely generated modules over commutative rings ⋮ The solvable conditions of linear system over commutative semirings ⋮ Characterizing when the rings \(R\) and \(R[T\) are integrally closed via linear equations over \(R\)] ⋮ A criterion for exactness of a complex of length two.

Cites Work

• Commutative rings whose finitely generated modules decompose
• Linear equations over a commutative ring
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