Bézout rings with almost stable range 1

DOI10.1016/j.jpaa.2007.05.026zbMath1159.13010OpenAlexW2084470188MaRDI QIDQ2457279

Warren Wm. McGovern

Publication date: 30 October 2007

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2007.05.026

zbMATH Keywords

stable rangeelementary divisor ringBézoutHermiteKaplansky

Mathematics Subject Classification ID

Commutative rings and modules of finite generation or presentation; number of generators (13E15) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Arithmetic rings and other special commutative rings (13F99)

Related Items (25)

Stable range conditions for abelian and duo rings ⋮ Bezout rings of stable range 1.5 ⋮ Reduction of matrices over simple Ore domains ⋮ Commutative domains of elementary divisors and some properties of their elements ⋮ Commutative Bézout domains of stable range 1.5 ⋮ Stable range and almost stable range ⋮ Generating solutions of a linear equation and structure of elements of the Zelisko group II ⋮ Kalman reduced form and pole placement by state feedback for multi‐input linear systems over Hermite rings ⋮ On Henriksen rings ⋮ J-Noetherian Bezout domain which is not of stable range 1 ⋮ Combining Euclidean and adequate rings ⋮ Commutative Bezout domains in which any nonzero prime ideal is contained in a finite set of maximal ideals ⋮ Diagonal matrix reduction over Hermite rings ⋮ Feebly projectable \(\ell \)-groups ⋮ Generating solutions of a linear equation and structure of elements of the Zelisko group ⋮ Equivalent generating pairs of an ideal of a commutative ring ⋮ Strongly stable rank and applications to matrix completion ⋮ Conditions for stable range of an elementary divisor rings ⋮ Unnamed Item ⋮ Elementary matrix reduction over Bézout domains ⋮ Equivalent generating vectors of finitely generated modules over commutative rings ⋮ Rings of dyadic range 1 ⋮ The Kaplansky condition and rings of almost stable range 1 ⋮ Elementary matrix reduction over J-stable rings ⋮ Elementary matrix reduction over certain rings

Cites Work

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• Some remarks on elementary divisor rings. II
• Neat rings
• Rings with many idempotents
• Complemented lattice-ordered groups
• Cozero complemented spaces; when the space of minimal prime ideals of a \(C(X)\) is compact
• Stable rank of rings and dimensionality of topological spaces
• Some Remarks About Elementary Divisor Rings
• Indecomposable Modules and Gelfand Rings
• Elementary Divisor Rings and Finitely Presented Modules
• Elementary Divisors and Modules
• The elementary divisor theorem for certain rings without chain condition
• Bezout domains with stable range 1

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