Stable rank of down-up algebras

Claudia Gallego; Andrea Solotar

doi:10.1016/j.jalgebra.2018.02.037

Stable rank of down-up algebras

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Resumen

We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra A(α,β,γ) has a non-free, stably free right ideal. Further, we compute the stable rank of these algebras using Stafford's Stable Range Theorem and Kmax dimension.

Idioma original	Inglés
Páginas (desde-hasta)	266-282
Número de páginas	17
Publicación	Journal of Algebra
Volumen	526
DOI	https://doi.org/10.1016/j.jalgebra.2018.02.037
Estado	Publicada - 15 may. 2019
Publicado de forma externa	Sí

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10.1016/j.jalgebra.2018.02.037

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title = "Stable rank of down-up algebras",

abstract = "We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra A(α,β,γ) has a non-free, stably free right ideal. Further, we compute the stable rank of these algebras using Stafford's Stable Range Theorem and Kmax dimension.",

keywords = "Down-up algebras, Kmax dimension, Krull dimension, Projective modules, Stable rank, Stably free modules",

author = "Claudia Gallego and Andrea Solotar",

note = "Publisher Copyright: {\textcopyright} 2018",

year = "2019",

month = may,

day = "15",

doi = "10.1016/j.jalgebra.2018.02.037",

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AU - Solotar, Andrea

PY - 2019/5/15

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N2 - We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra A(α,β,γ) has a non-free, stably free right ideal. Further, we compute the stable rank of these algebras using Stafford's Stable Range Theorem and Kmax dimension.

AB - We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra A(α,β,γ) has a non-free, stably free right ideal. Further, we compute the stable rank of these algebras using Stafford's Stable Range Theorem and Kmax dimension.

KW - Down-up algebras

KW - Kmax dimension

KW - Krull dimension

KW - Projective modules

KW - Stable rank

KW - Stably free modules

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U2 - 10.1016/j.jalgebra.2018.02.037

DO - 10.1016/j.jalgebra.2018.02.037

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VL - 526

SP - 266

EP - 282

JO - Journal of Algebra

JF - Journal of Algebra

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Stable rank of down-up algebras

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