Maximal sublattices and Frattini sublattices of bounded lattices

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)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Schmid, Jürg

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:

25 Jul 2020 14:22

Publisher DOI:

10.1017/S1446788700000355

BORIS DOI:

10.7892/boris.115325

URI:

https://boris.unibe.ch/id/eprint/115325

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