INJECTIVE MODULES OVER DOWN-UP ALGEBRAS

CARVALHO, PAULA A. A. B. ; LOMP, CHRISTIAN ; PUSAT-YILMAZ, DILEK

Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 53-59

Résumé

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.

Détail

DOI : 10.1017/S0017089510000261

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