Download this article
 Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Global dimension of real-exponent polynomial rings

Nathan Geist and Ezra Miller

Vol. 17 (2023), No. 10, 1779–1788

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 = R𝔪 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 n satisfying a mild density condition.

global dimension, homological dimension, flat dimension, polynomial ring, real-exponent polynomial, commutative ring, monoid algebra, real cone, quantum noncommutative toric variety, persistent homology
Mathematical Subject Classification
Primary: 05E40, 06F05, 13D02, 13D05, 13F20
Secondary: 13P25, 14A22, 55N31, 62R40
Received: 25 September 2021
Revised: 16 May 2022
Accepted: 17 October 2022
Published: 19 September 2023
Nathan Geist
Mathematics Department
Duke University
Durham, NC
United States
Ezra Miller
Mathematics Department
Duke University
Durham, NC
United States

Open Access made possible by participating institutions via Subscribe to Open.