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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2011 Volume 17, Number 4, Pages 278–292 (Mi timm770)

On finite critical lattices. II

O. E. Perminova

Ural Federal 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 lattices for $n=7$ and $n\geq9$.

Keywords: lattice, sublattice, endomorphism, critical lattice.

UDC: 512.562



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