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2018 Finite atomic lattices and their monomial ideals
Peng He, Xue-ping Wang
Rocky Mountain J. Math. 48(8): 2503-2542 (2018). DOI: 10.1216/RMJ-2018-48-8-2503

Abstract

This paper primarily studies monomial ideals by their associated lcm-lattices. It first introduces notions of weak coordinatizations of finite atomic lattices which have weaker hypotheses than coordinatizations and shows the characterizations of all such weak coordinatizations. It then defines a finite super-atomic lattice in $\mathcal {L}(n)$, investigates the structures of $\mathcal {L}(n)$ by their super-atomic lattices and proposes an algorithm to calculate all of the super-atomic lattices in $\mathcal {L}(n)$. It finally presents a specific labeling of finite atomic lattice and obtains the conditions that the specific labelings of finite atomic lattices are the weak coordinatizations or the coordinatizations by using the terminology of super-atomic lattices.

Citation

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Peng He. Xue-ping Wang. "Finite atomic lattices and their monomial ideals." Rocky Mountain J. Math. 48 (8) 2503 - 2542, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2503

Information

Published: 2018
First available in Project Euclid: 30 December 2018

zbMATH: 06999272
MathSciNet: MR3894991
Digital Object Identifier: 10.1216/RMJ-2018-48-8-2503

Subjects:
Primary: 06D05, 13D02

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 8 • 2018
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