Geodesic
Valuations on modular lattices
Mathematica Bohemica, Tome 116 (1991) no. 4, pp. 391-395

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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.
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.
DOI : 10.21136/MB.1991.126021
Classification : 06C05
Keywords: modular lattices; prime quotients; order-dense quotients; valuation; discrete valuation 
Jakubík, Ján. Valuations on modular lattices. Mathematica Bohemica, Tome 116 (1991) no. 4, pp. 391-395. doi: 10.21136/MB.1991.126021
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