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The ring R of real-exponent polynomials in n variables over any field hasglobal 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 aKoszul-like resolution. Projective and flat resolutions of all R-modules areconstructed from this resolution of k. The same results hold when R is replacedby the monoid algebra for the positive cone of any subgroup of $\mathbb{R}^n$satisfying a mild density condition.

Global dimension of real-exponent polynomial rings