Geodesic
INJECTIVE MODULES OVER DOWN-UP ALGEBRAS
Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 53-59

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DOI

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. 
CARVALHO, PAULA A. A. B.; LOMP, CHRISTIAN; PUSAT-YILMAZ, DILEK. INJECTIVE MODULES OVER DOWN-UP ALGEBRAS. Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 53-59. doi: 10.1017/S0017089510000261
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     title = {INJECTIVE {MODULES} {OVER} {DOWN-UP} {ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {53--59},
     year = {2010},
     volume = {52},
     number = {A},
     doi = {10.1017/S0017089510000261},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000261/}
}
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