On duality of submodule lattices

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2000 English Publisher:University of Zielona Góra, PolandJournal:Discussiones Mathematicae - General Algebra and Applications, volume 20, page 43 (issn: 1509-9415, eissn: 2084-0373,

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Authors: Czédli, Gábor; Takách, Géza;

doi: 10.7151/dmgaa.1004

On duality of submodule lattices

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Abstract

\textit{G. Hutchinson} [Proc. Univ. Houston, Lattice Theory Conf., Houston 1973, 69-94 (1973; Zbl 0302.06016)] has shown that the equational theory of an infinite rank free module is self-dual. Here, an elementary proof is given based on the diagonalization of integer matrices and the self-duality of subgroup lattices of finite Abelian groups (for which a short proof is given, too).

Keywords

Finite abelian groups, Modular lattices, Desarguesian lattices, subgroup lattices of finite Abelian groups, submodule lattice, duality, lattice identity

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