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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.

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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