Email this article Finiteness of a 3-Generated Lattice with Seminormal and Coseminormal Elements Among Generators
- Authors: Shushpanov M.P.1
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Affiliations:
- El’tsin Ural Federal University
- Issue: Vol 57, No 3 (2018)
- Pages: 237-247
- Section: Article
- URL: https://journals.rcsi.science/0002-5232/article/view/234091
- DOI: https://doi.org/10.1007/s10469-018-9496-3
- ID: 234091
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Abstract
It is known that a modular 3-generated lattice is always finite and contains at most 28 elements. Lattices generated by three elements with certain modularity properties may no longer be modular but nevertheless remain finite. It is shown that a 3-generated lattice among generating elements of which one is seminormal and another is coseminormal is finite and contains at most 45 elements. This estimate is stated to be sharp.
About the authors
M. P. Shushpanov
El’tsin Ural Federal University
Author for correspondence.
Email: Mikhail.Shushpanov@gmail.com
Russian Federation, ul. Mira 19, Yekaterinburg, 620002
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