Tate resolution and the structure of the exact local ring
Tate resolutions for commutative graded algebras over a local ring
Tensor complexes: multilinear free resolutions constructed from higher tensors
The most fundamental complexes of free modules over a commutative ring are the Koszul complex, which is constructed from a vector (i.e., a 1-tensor), and the Eagon-Northcott and Buchsbaum-Rim complexes, which are constructed from a matrix (i.e., a 2-tensor). The subject of this paper is a multilinear analogue of these complexes, which we construct from an arbitrary higher tensor. Our construction provides detailed new examples of minimal free resolutions, as well as a unifying view on a wide variety...
Tensor products of modules and the rigidity of Tor.
Tensor products of modules, rigidity and local cohomology.
Tensor products of symmetric functions over ℤ2
We calculate the homology and the cycles in tensor products of algebras of symmetric function over ℤ2
Testing flatness and computing rank of a module using syzygies
Using syzygies computed via Gröbner bases techniques, we present algorithms for testing some homological properties for submodules of the free module , where A = R[x₁,...,xₙ] and R is a Noetherian commutative ring. We will test if a given submodule M of is flat. We will also check if M is locally free of constant dimension. Moreover, we present an algorithm that computes the rank of a flat submodule M of and also an algorithm that computes the projective dimension of an arbitrary submodule...
The amalgamated duplication of a ring along a semidualizing ideal
The André-Quillen homology of commutative graded algebras
The Brauer Group of A [T].
The category of cofinite modules for ideals of dimension one and codimension one
The cohomological dimension of the ordered set of real numbers equals three
The cohomological dimension of the quotient field of the two dimensional complete local domain
The Conductor of one-dimensional Gorenstein Rings in their blowing-up.
The cones associated to some tranversal polymatroids.
The connection between a conjecture of Carlisle and Kropholler, now a theorem of Benson and Crowley-Boevey, and Grothendieck's Riemannian-Roch and duality theorems.
The Construction of a Module of Finite Projective Dimension from a Finitely Generated Module of Finite Injective Dimension.
The cyclic homology and K-theory of curves.
The Elements of K2 (...s).
The embedding dimension of the formal Moduli space of certain curve singularities.