Abstract
Let R be a ring, M a left R-module. We say that M has Krull dimension, resp. Gabriel dimension, if the lattice L(M) has Krull dimension, resp. Gabriel dimension. The ordinal Kdim L(M), resp. Gdim L(M), will be denoted by Kdim M, resp. Gdim M, and it is called the Krull dimension, resp. Gabriel dimension, of M.
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