Journal of the
Korean Mathematical Society JKMS

This paper is a natural continuation of [2], [3], [4] and [5]. Localization techniques for modular lattices are developed. These techniques are applied to study liftings of linear order types from quotient lattices and to find $\Gamma$--dense sets in certain lattices without $\Gamma$--deviation in the sense of [4], where $\Gamma$ is a set of indecomposable linear order types.

Keywords: poset, modular lattice, quotient lattice, Krull dimension, dual Krull dimension, $\Gamma$--deviation, Serre class, hereditary torsion theory, localization

MSC numbers: 06A11, 06B23, 06C05, 16P60, 18E15, 18E35, 18E40