Stable rank of down-up algebras

Claudia Gallego; Andrea Solotar

doi:10.1016/j.jalgebra.2018.02.037

Stable rank of down-up algebras

Claudia Gallego
, Andrea Solotar

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	266-282
Number of pages	17
Journal	Journal of Algebra
Volume	526
DOIs	https://doi.org/10.1016/j.jalgebra.2018.02.037
State	Published - 15 May 2019
Externally published	Yes

Keywords

Down-up algebras
Kmax dimension
Krull dimension
Projective modules
Stable rank
Stably free modules

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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.",

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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

UR - https://www.scopus.com/pages/publications/85062157778

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DO - 10.1016/j.jalgebra.2018.02.037

M3 - Article

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SN - 0021-8693

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SP - 266

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Stable rank of down-up algebras

Abstract

Keywords

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