-flat and -FP-injective modules
In this paper, we study the existence of the -flat preenvelope and the -FP-injective cover. We also characterize -coherent rings in terms of the -FP-injective and -flat modules.
Nagata rings and directed unions of Artinian subrings.
Noncommutative del Pezzo surfaces and Calabi-Yau algebras
The hypersurface in with an isolated quasi-homogeneous elliptic singularity of type , has a natural Poisson structure. We show that the family of del Pezzo surfaces of the corresponding type provides a semiuniversal Poisson deformation of that Poisson structure. We also construct a deformation-quantization of the coordinate ring of such a del Pezzo surface. To this end, we first deform the polynomial algebra to a noncommutative algebra with generators and the following 3 relations labelled...
Non-embeddable -convex manifolds
We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable -convex manifold.We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type . To this end we study small resolutions of -singularities.
Non-free Projective Modules Over IH[X, Y] and Stable Bundles Over IP2(...).
Non-Noetherian Rings for which Each Proper Subring is Noetherian.
Normal and tangential flatness.
Note on modules over Prüfer domains.
Note on projective modules.
Notes on an extension of Krull's principal ideal theorem
Notes on radical filters of ideals
Notes on the multiplicity conjecture.
New cases of the multiplicity conjecture are considered.