We study finite dimensional representations over some Noetherian algebras a field of characteristic zero. More precisely, we give necessary and sufficient conditions for the category locally to be closed under taking injective hulls extend results known group rings enveloping Ore extensions, Hopf crossed products, affine low Gelfand-Kirillov dimension.

Example 1.1. Let C ⊆ Ak be the nodal cubic plane curve given by y 2 = x + x, where k is some algebraically closed field. Let C̃ be its normalization; then C̃ ∼= A. Finally, let D be the open subcurve of C̃ obtained by removing one of the two points lying over the node of C. We consider the morphism D → Ak. Via an explicit parametric form, it is easy to check that this morphism is injective both on...

In the category of operator spaces, that is, subspaces of the bounded linear operators B(H) on a complex Hilbert space H together with the induced matricial operator norm structure, objects are equivalent if they are completely isometric, i.e. if there is a linear isomorphism between the spaces which preserves this matricial norm structure. Since operator algebras, that is, subalgebras of B(H),...

We investigate the notion of the C-projective dimension of a module, where C is a semidualizing module. When C = R, this recovers the standard projective dimension. We show that three natural definitions of finite Cprojective dimension agree, and investigate the relationship between relative cohomology modules and absolute cohomology modules in this setting. Finally, we prove several results th...

In this paper we study some properties of GC -projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC -projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

We prove that the relative commutant of a diffuse von Neumann subalgebra in a hyperbolic group von Neumann algebra is always injective. It follows that any non-injective subfactor in a hyperbolic group von Neumann algebra is non-Γ and prime. The proof is based on C∗-algebra theory.

The main theorem of [4] say that there is a proper closed simplicial model category structure on the category Spt of symmetric spectra, and that the associated homotopy category Ho(Spt) is equivalent to the stable category. This paper shows how to generalize this result to the category PreSpt(C) of presheaves of symmetric spectra on an arbitrary small Grothendieck site C. The reader will observ...

We prove that any separable exact C*-algebra is isomorphic to a subalgebra of the Cuntz algebra O2. We further prove that if A is a simple separable unital nuclear C*-algebra, then O2 ⊗ A ∼= O2, and if, in addition, A is purely infinite, then O∞ ⊗ A ∼= A. The embedding of exact C*-algebras in O2 is continuous in the following sense. If A is a continuous field of C*-algebras over a compact manif...