This article is cited in 3 papers

On finite critical lattices

O. E. Perminova

Ural State University

Abstract: Critical lattices are considered, i.e., lattices without nontrivial endomorphisms and not containing nontrivial proper sublattices without nontrivial endomorphisms. It is proved that there exist $n$-element critical sublattices for any $n\ge21$.

Keywords: lattice, sublattice, endomorphism, critical lattice.

UDC: 512.562

Received: 12.02.2009

 English version: Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2009, 267, suppl. 1, S192–S200

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