Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2504.05507 |
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Inhaltsangabe:
- This paper explores alternative statements of the axioms for lattice gluing, focusing on lattices that are modular, locally finite, and have finite covers, but may have infinite height. We give a set of "maximal" axioms that maximize what can be immediately adduced about the structure of a valid gluing. We also give a set of "minimal" axioms that minimize what needs to be adduced to prove that a system of blocks is a valid gluing. This system appears to be novel in the literature. A distinctive feature of the minimal axioms is that they involve only relationships between elements of the skeleton which are within an interval $[x \wedge y, x \vee y]$ where either $x$ and $y$ cover $x \wedge y$ or they are covered by $x \vee y$. That is, they have a decidedly local scope, despite that the resulting sum lattice, being modular, has global structure, such as the diamond isomorphism theorem.