Global dimension of real-exponent polynomial rings
arXiv:2109.04924 · doi:10.2140/ant.2023.17.1779
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 satisfying a mild density condition.
v2: 10 pages, 2 figures; new Example 2.3 (containing both Figures) and Example 4.2. v1: 8 pages, no figures