#### 122 Citations

Symmetric polynomials in the variety generated by Grassmann algebras

- Mathematics
- Journal of Algebra and Its Applications
- 2021

Let [Formula: see text] denote the variety generated by infinite-dimensional Grassmann algebras, i.e. the collection of all unitary associative algebras satisfying the identity [Formula: see text],… Expand

J an 2 01 9 From analytical mechanical problems to rewriting theory through

- 2018

This note surveys the historical background of the Gröbner basis theory for D-modules and linear rewriting theory. The objective is to present a deep interaction of these two fields largely developed… Expand

From analytical mechanical problems to rewriting theory through M. Janet

- Mathematics
- 2017

This note surveys the historical background of the Gröbner basis theory for D-modules and linear rewriting theory. The objective is to present a deep interaction of these two fields largely developed… Expand

Properties of the resolution of almost Gorenstein algebras

- Mathematics
- 2020

We study properties of the resolution of almost Gorenstein artinian algebras $R/I,$ i.e. algebras defined by ideals $I$ such that $I=J+(f),$ with $J$ Gorenstein ideal and $f\in R.$ Such algebras… Expand

Geometrically Reductive Groups and Finitely Generated Rings of Invariants

- 2017

We discuss when rings of invariants of algebras over an algebraically closed field are finitely generated. We prove Nagata’s Theorem, which states that geometrically reductive groups have finitely… Expand

Conditions for Additional Roots from Maximal-Rank Minors of Macaulay Matrices

- Mathematics
- 2009

Necessary conditions, under which the maximal-rank minors of a (possibly singular) Macaulay matrix of a polynomial system vanish, are analyzed. It is shown that the vanishing of the maximal-rank… Expand

Ein Beweis des Hilbertschen Basissatzes.

- Mathematics
- 1976

Der Basissatz von Hubert [2] besagt: Ist ein kommutativer Ring R mit Einselement ein Noether-Ring, so auch der zugehörige Polynomring R[x]. Der folgende Beweis scheint bisher nicht in der Literatur… Expand

$\mathbb{Z}_k^{(r)}$-Algebras, FQH Ground States, and Invariants of Binary Forms

- Physics, Mathematics
- 2021

A prominent class of model FQH ground states is those realized as correlation function of Z k -algebras. In this paper, we study the interplay between these algebras and their corresponding… Expand

August 2021 SYZYGIES OVER A POLYNOMIAL RING

- 2021

We discuss results and open problems on graded minimal Free Resolutions over polynomial rings.