Finite atomic lattices and resolutions of monomial ideals

Sonja Mapes*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated lcm-lattices. In particular, we formally define the notion of coordinatizing a finite atomic lattice P to produce a monomial ideal whose lcm-lattice is P, and we give a characterization of all such coordinatizations. We prove that all relations in the lattice L(n) of all finite atomic lattices with n ordered atoms can be realized as deformations of exponents of monomial ideals. We also give structural results for L(n). Moreover, we prove that the cellular structure of a minimal free resolution of a monomial ideal M can be extended to minimal resolutions of certain monomial ideals whose lcm-lattices are greater than that of M in L(n).

Original languageEnglish (US)
Pages (from-to)259-276
Number of pages18
JournalJournal of Algebra
Volume379
DOIs
StatePublished - Apr 1 2013

Keywords

  • Cellular resolutions
  • Finite atomic lattices
  • Minimal free resolutions
  • Monomial ideals

ASJC Scopus subject areas

  • Algebra and Number Theory

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