Decompositions of commutative monoid congruences and binomial ideals

Published

Journal Article

©2014 Mathematical Sciences Publishers. 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.

Full Text

Duke Authors

Cited Authors

  • Kahle, T; Miller, E

Published Date

  • January 1, 2014

Published In

Volume / Issue

  • 8 / 6

Start / End Page

  • 1297 - 1364

International Standard Serial Number (ISSN)

  • 1937-0652

Digital Object Identifier (DOI)

  • 10.2140/ant.2014.8.1297

Citation Source

  • Scopus