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. 110127. 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) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics 
UniBE Contributor: 
Schmid, Jürg 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
14467887 
Publisher: 
Cambridge University Press 
Language: 
English 
Submitter: 
Marceline Brodmann 
Date Deposited: 
21 Jul 2020 09:04 
Last Modified: 
25 Jul 2020 14:22 
Publisher DOI: 
10.1017/S1446788700000355 
BORIS DOI: 
10.7892/boris.115325 
URI: 
https://boris.unibe.ch/id/eprint/115325 