Vol. 8, No. 6, 2014

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

Volume 12
Issue 7, 1559–1821
Issue 6, 1311–1557
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

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' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Decompositions of commutative monoid congruences and binomial ideals

Thomas Kahle and Ezra Miller

Vol. 8 (2014), No. 6, 1297–1364

Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences, introduced here complete with witnesses and associated prime objects. The combinatorial theory of mesoprimary decomposition lifts to arbitrary binomial ideals in monoid algebras. The resulting binomial mesoprimary decomposition is a new type of intersection decomposition for binomial ideals that enjoys computational efficiency and independence from ground field hypotheses. Binomial primary decompositions are easily recovered from mesoprimary decomposition.

commutative monoid, monoid congruence, primary decomposition, mesoprimary decomposition, binomial ideal, coprincipal ideal, associated prime
Mathematical Subject Classification 2010
Primary: 20M14, 05E40, 20M25
Secondary: 20M30, 20M13, 05E15, 13F99, 13C05, 13P99, 13A02, 68W30, 14M25, 20M14, 05E40
Received: 8 February 2012
Revised: 13 May 2014
Accepted: 18 June 2014
Published: 2 October 2014
Thomas Kahle
Fakultät für Mathematik
Otto-von-Guericke Universität Magdeburg
Institut Algebra und Geometrie
D-39106 Magdeburg
Ezra Miller
Mathematics Department
Duke University
Durham, NC 27708
United States