Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 55, No. 3, pp. 373-380 (1998)

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Complements in Modular and Semimodular Lattices

Gabriela Hauser Bordalo and Elias Rodrigues

Centro de Álgebra da Universidade de Lisboa (C.A.U.L.),
Av. Professor Gama Pinto, 2, 1699 Lisboa Codex - PORTUGAL
E-mail: mchauser@ptmat.lmc.fc.ul.pt Univ. da Madeira, Departamento de Matemática,
Colégio dos Jesuitas, Largo do Município, 9000 Funchal - PORTUGAL
E-mail: elias@dragoeiro.uma.pt

Abstract: We study the relations between the complements of $a$ and $b$ when $a$ is covered by $b$ on finite upper-semimodular lattices and when $a<b$ on modular lattices. We give some results that generalize the well known properties of complements in distibutive lattices. From there, we derive a property of semisimple $R$-modules.

Keywords: Modular lattices; semimodular lattices; complemented lattices.

Classification (MSC2000): 06B, 06C

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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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