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INJECTIVE MODULES OVER DOWN-UP ALGEBRAS

Published online by Cambridge University Press:  24 June 2010

PAULA A. A. B. CARVALHO ,
CHRISTIAN LOMP  and
DILEK PUSAT-YILMAZ
PAULA A. A. B. CARVALHO
Affiliation:
Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
CHRISTIAN LOMP
Affiliation:
Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
DILEK PUSAT-YILMAZ
Affiliation:
Department of Mathematics, Izmir Institute of Technology, 35430 Gulbahce, Urla-Izmir, Turkey
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Abstract

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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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