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Citation - WoS: 14
Citation - Scopus: 12
Injective modules over down-up algebras
(Cambridge University Press, 2010) Carvalho, Paula A.A.B.; Lomp, Christian; Pusat, Dilek
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.
Citation - WoS: 16
Citation - Scopus: 14
Rings Whose Modules Are Weakly Supplemented Are Perfect. Applications To Certain Ring Extensions
(Mathematica Scandinavica, 2009) Büyükaşık, Engin; Lomp, Christian
In this note we show that a ring R is left perfect if and only if every left R-module is weakly supplemented if and only if R is semilocal and the radical of the countably infinite free left R-module has a weak supplement.

Mathematics / Matematik