Gaussian elements of a semicontent algebra
Abstract
The connection between a univariate polynomial having locally principal content and the content function acting like a homomorphism (the so-called Gaussian property) has been explored by many authors. In this work, we extend several such results to the contexts of multivariate polynomials, power series over a Noetherian ring, and base change of affine -algebras by separable algebraically closed field extensions. We do so by using the framework of the Ohm-Rush content function. The correspondence is particularly strong in cases where the base ring is approximately Gorenstein or the element of the target ring is regular.
Cite
@article{arxiv.1708.02364,
title = {Gaussian elements of a semicontent algebra},
author = {Neil Epstein and Jay Shapiro},
journal= {arXiv preprint arXiv:1708.02364},
year = {2017}
}
Comments
Removed a superfluous proposition, as a more general version already exists in the literature; added a corollary at the end and a reference to it in the Main Results block on page 2; changed the title and abstract slightly; cleaned up some things. 13 pages. Comments still welcome!