Rocky Mountain Journal of Mathematics

On mesoprimary decomposition of monoid congruences

Christopher O'Neill

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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

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

First available in Project Euclid: 24 November 2018

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Zentralblatt MATH identifier

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

Binomial ideal monoid congruence mesoprimary decomposition poset


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.

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  • 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.