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arXiv · 2109.04924

Global dimension of real-exponent polynomial rings

Nathan Geist·Ezra Miller
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Abstract

The ring R of real-exponent polynomials in n variables over any field has global dimension n+1 and flat dimension n. In particular, the residue field k = R/m of R modulo its maximal graded ideal m has flat dimension n via a Koszul-like resolution. Projective and flat resolutions of all R-modules are constructed from this resolution of k. The same results hold when R is replaced by the monoid algebra for the positive cone of any subgroup of $\mathbb{R}^n$ satisfying a mild density condition.

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Nathan Geist, Ezra Miller. 2021-09-10. Global dimension of real-exponent polynomial rings. https://doi.org/10.2140/ant.2023.17.1779

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