Rocky Mountain Journal of Mathematics

On mesoprimary decomposition of monoid congruences

Christopher O'Neill

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We prove two main results concerning mesoprimary decomposition of monoid congruences, as introduced by Kahle and Miller. First, we identify which associated prime congruences appear in every mesoprimary decomposition, thereby completing the theory of mesoprimary decomposition of monoid congruences as a more faithful analogue of primary decomposition. Second, we answer a question posed by Kahle and Miller by characterizing which finite posets arise as the set of associated prime congruences of monoid congruences.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 6 (2018), 2069-2085.

Dates
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1543028453

Digital Object Identifier
doi:10.1216/RMJ-2018-48-6-2069

Mathematical Reviews number (MathSciNet)
MR3879317

Zentralblatt MATH identifier
06987240

Subjects
Primary: 05E40: Combinatorial aspects of commutative algebra 06A07: Combinatorics of partially ordered sets 20M14: Commutative semigroups

Keywords
Binomial ideal monoid congruence mesoprimary decomposition poset

Citation

O'Neill, Christopher. On mesoprimary decomposition of monoid congruences. Rocky Mountain J. Math. 48 (2018), no. 6, 2069--2085. doi:10.1216/RMJ-2018-48-6-2069. https://projecteuclid.org/euclid.rmjm/1543028453


Export citation

References

  • D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Grad. Texts Math. 150 (1995).
  • P. Grillet, Commutative semigroups, Adv. Math., Kluwer Academic Publishers, London, 2001.
  • T. Kahle and E. Miller, Decompositions of commutative monoid congruences and binomial ideals, Alg. Num. Th. 8 (2014), 1297–1364.
  • L. Matusevich and C. O'Neill, Some algebraic aspects of mesoprimary decomposition, J. Pure Appl. Alg., arXiv:math.AC/1706.07496.
  • C. O'Neill, Monoid congruences, binomial ideals, and their decompositions, Ph.D. dissertation, Duke University, Durham, NC, 2014.