## 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 language | English (US) |
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Pages (from-to) | 259-276 |

Number of pages | 18 |

Journal | Journal of Algebra |

Volume | 379 |

DOIs | |

State | Published - Apr 1 2013 |

## Keywords

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

## ASJC Scopus subject areas

- Algebra and Number Theory