Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type.

DOI10.1134/S0037446615040072zbMath1338.06007MaRDI QIDQ748472

A. G. Gein, Mikhaĭl P. Shushpanov

Publication date: 29 October 2015

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

modular latticesmodularitymodular elementsfree modular latticessublattices generated by three elements

Mathematics Subject Classification ID

Semimodular lattices, geometric lattices (06C10) Structure theory of lattices (06B05) Modular lattices, Desarguesian lattices (06C05) Free lattices, projective lattices, word problems (06B25)

Related Items

Modularity and distributivity of 3-generated lattices with special elements among generators ⋮ On infinity of the free 3-generated lattice with one left modular generator ⋮ On 3-generated lattices with a completely modular element among generators ⋮ On the embedding of the free lattice of rank 3 in the lattice freely generated by three completely right modular elements ⋮ Finiteness of a 3-generated lattice with seminormal and coseminormal elements among generators ⋮ Free 3-generated lattices with two semi-normal generators ⋮ On the finiteness of a 3-generated lattice with left modular and separating elements among generators ⋮ 3-generated lattice with left modular and separating generators ⋮ Finitely generated lattices with completely modular elements among generators.

Cites Work

• Defining relations of a free modular lattice of rank 3
• A characterization of neutral elements by the exclusion of sublattices
• Finitely generated lattices with completely modular elements among generators.
• Standard ideals in lattices
• On the Theorem of Jordan-Holder
• Unnamed Item

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