The Kaplansky condition and rings of almost stable range 1

DOI10.1090/S0002-9939-2013-11567-4zbMath1281.13013arXiv1107.3000OpenAlexW1994618188MaRDI QIDQ2845450

Moshe Roitman

Publication date: 30 August 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3000

zbMATH Keywords

elementary divisor ring\(K\)-Hermitealmost stable rang 1Kaplansky conditionstable rang

Mathematics Subject Classification ID

Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Arithmetic rings and other special commutative rings (13F99)

Related Items (10)

Stable range and almost stable range ⋮ Combining Euclidean and adequate rings ⋮ Diagonal matrix reduction over Hermite rings ⋮ On the existence of unimodular matrices with a prescribed submatrix ⋮ Strongly stable rank and applications to matrix completion ⋮ Elementary matrix reduction over Bézout domains ⋮ Diagonal reduction of matrices over commutative semihereditary Bezout rings ⋮ Rings of dyadic 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
• Arithmetic properties in pullbacks
• On regular rings with stable range 2
• The construction \(D+XD_s[X\)]
• Bézout rings with almost stable range 1
• Rings of Continuous Functions in Which Every Finitely Generated Ideal is Principal
• Some Remarks About Elementary Divisor Rings
• Elementary Divisors and Modules

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