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Unions of uniquely complemented lattices

Ján Jakubík (1997)

Mathematica Bohemica

In this paper we generalize a result of V. N. Salij concerning direct product decompositions of lattices which are complete and uniquely complemented.

Valuations on modular lattices

Ján Jakubík (1991)

Mathematica Bohemica

It is well-known that there exist infinite modular lattices possessing no non-trivial valuations. In this paper a class 𝒦 of modular lattices is defined and it is proved that each lattice belonging to 𝒦 has a nontrivial valuation. Next, a result of G . Birkhoff concerning valuations on modular lattices of finite length is generalized.

Weak congruences of an algebra with the CEP and the WCIP

Andrzej Walendziak (2002)

Czechoslovak Mathematical Journal

Here we consider the weak congruence lattice C W ( A ) of an algebra A with the congruence extension property (the CEP for short) and the weak congruence intersection property (briefly the WCIP). In the first section we give necessary and sufficient conditions for the semimodularity of that lattice. In the second part we characterize algebras whose weak congruences form complemented lattices.

When does an AB5* module have finite hollow dimension?

Derya Keskin Tütüncü, Rachid Tribak, Patrick F. Smith (2011)

Colloquium Mathematicae

Using a lattice-theoretical approach we find characterizations of modules with finite uniform dimension and of modules with finite hollow dimension.

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