DIMENSIONAL GROUPS AND FIELDS

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimension. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that a pseudofinite (m) over tilde (c)-group of finite positive dimension contains a finite-by-abelian subgroup of positive dimension, and a pseudofinite group of dimension 2 contains a soluble subgroup of dimension 2.