Valuations on modular lattices
Ján Jakubík · Mathematica Bohemica · 1991
It is well-known that there exist infinite modular lattices possessing no non-trivial valuations. In this paper a class $\Cal K$ of modular lattices is defined and it is proved that each lattice belonging to $\Cal K$ has a nontrivial valuation. Next, a result of $G$. Birkhoff concerning valuations on modular lattices of finite length is generalized.