Adams, M. E.; Freese, Ralph; Nation, J. B.; Schmid, Jürg (1997). Maximal sublattices and Frattini sublattices of bounded lattices. Journal of the Australian Mathematical Society, 63(1), pp. 110-127. Cambridge University Press 10.1017/S1446788700000355
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We investigate the number and size of the maximal sublattices of a finite lattice. For any positive integer k, there is a finite lattice L with more that ]L]k sublattices. On the other hand, there are arbitrary large finite lattices which contain a maximal sublattice with only 14 elements. It is shown that every bounded lattice is isomorphic to the Frattini sublattice (the intersection of all maximal sublattices) of a finite bounded lattice.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Schmid, Jürg (A) |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1446-7887 |
Publisher: |
Cambridge University Press |
Language: |
English |
Submitter: |
Marceline Brodmann |
Date Deposited: |
21 Jul 2020 09:04 |
Last Modified: |
29 Mar 2023 23:36 |
Publisher DOI: |
10.1017/S1446788700000355 |
BORIS DOI: |
10.7892/boris.115325 |
URI: |
https://boris.unibe.ch/id/eprint/115325 |
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