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We consider the derived category of a specific non-Noetherian ring \Lambda, and show that there are objects in D(\Lambda) that are not Bousfield equivalent to any module. This answers a question posed...
Abstract: Let $M$ be a module. A {\em $\delta$-cover} of $M$ is an epimorphism from a module $F$ onto $M$ with a $\delta$-small kernel. A $\delta$-cover is said to be a {\em flat $\delta$-cover} in ca...
In this paper, we extend some problems from Arens regularity and module Arens regularity of Banach algebras to module actions.
We determine the graded composition multiplicity in the symmetric algebra S•(V ) of the natural GLn(q)-module V , or equivalently in the coinvariant algebra of V ,for a large class of irreducibl...
In this paper we study relations between the exchange relations in the cluster algebra of type-An, which has the 1-skeleton of the associahedron as its exchange graph, and the complex of triangulation...
Transformation of operator algebras under Hopf algebra twist is studied. It is shown that that adjoint module algebras are stable under the twist. Applications to vector fields on non-commutative spac...
We obtain a projective submodule of Lie(n) in prime char-acteristic p for n not a p-power, and show that the ratio of its dimension to that of Lie(n) approaches 1 as n tends to infinity.
We determine the invariants, with arbitrary determinant twists, of the par-abolic subgroups of the finite general linear group GLn(q) acting on the tensor product of the symmetric algebra S•(V )...
A module M is called hollow-lifting if every submodule N of M such that M/N is hollow contains a direct summand D \subseteq N such that N/D is a small submodule of M/D. A module M is called lifting if...
A well-known result of Kostant gives a description of the G-module structure for the exterior algebra of Lie algebra $\frak g$. We give a generalization of this result for the isotropy representation...

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