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arXiv · 1708.02364

Gaussian elements of a semicontent algebra

Neil Epstein·Jay Shapiro
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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 $K$-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.

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Neil Epstein, Jay Shapiro. 2017-08-08. Gaussian elements of a semicontent algebra. https://arxiv.org/abs/1708.02364

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