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INJECTIVE MODULES OVER DOWN-UP ALGEBRAS
Published online by Cambridge University Press: 24 June 2010
Abstract
The purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.
- Type
- Research Article
- Information
- Glasgow Mathematical Journal , Volume 52 , Issue A: Rings and Modules in Honour of Patrick F. Smith's 65th Birthday , July 2010 , pp. 53 - 59
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 2010
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