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On balanced lattices and Goldie dimension of balanced lattices. (English. Russian original) Zbl 0851.06002

Sib. Math. J. 35, No. 3, 539-546 (1994); translation from Sib. Mat. Zh. 35, No. 3, 602-611 (1994).
The main purpose of the present note is to extend certain results on Goldie numbers to some class of lattices which is broader than the class of modular lattices. The class mentioned is the class of balanced lattices. We establish a relation between the Goldie number and the Helly and Radon numbers. We call a lattice \(L\) balanced if for any elements \(x,y,z \in L\) the conditions \(y \wedge z = 0\) and \(x \wedge (y \vee z) = 0\) imply that \(y \wedge (x \vee z) = 0\).

MSC:

06B05 Structure theory of lattices
06C05 Modular lattices, Desarguesian lattices
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