58 citations · 399 across the 82 of their papers we have counts for
68 papers · 1 filter
Computing Gröbner Bases and Free Resolutions of OI-Modules
Michael Morrow, Uwe Nagel
Given a sequence of related modules defined over a sequence of related polynomial rings, one may ask how to simultaneously compute a finite Gröbner basis for each . Furt…
Buchsbaum-Eisenbud complexes of OI-modules
Nathan Fieldsteel, Uwe Nagel
We extend the theory of Koszul and Buchsbaum-Eisenbud complexes to modules over commutative OI-algebras and show that they still have the familiar properties of the classical compl…
Shift Invariant Algebras, Segre Products and Regular Languages
Aida Maraj, Uwe Nagel
Motivated by results on the rationality of equivariant Hilbert series of some hierarchical models in algebraic statistics we introduce the Segre product of formal languages and app…
A formula for symbolic powers
Paolo Mantero, Cleto B. Miranda-Neto, Uwe Nagel
Let be a Cohen-Macaulay ring which is local or standard graded over a field, and let be an unmixed ideal that is also generically a complete intersection. Our goal in this…
Minimal and cellular free resolutions over polynomial OI-algebras
Nathan Fieldsteel, Uwe Nagel
Minimal free resolutions of graded modules over a noetherian polynomial ring have been attractive objects of interest for more than a hundred years. We introduce and study two natu…
Rationality of Equivariant Hilbert Series and Asymptotic Properties
Uwe Nagel
An FI- or an OI-module over a corresponding noetherian polynomial algebra may be thought of as a sequence of compatible modules over a poly…