Draft:Unbounded generating number

See rank condition

In mathematics, more specifically in the field of ring theory, a ring R has unbounded generating number (UGN) if, for each positive integer m, any set of generators for the free right R-module Rm has cardinality ≥m.

Rings with unbounded generating number have in the literature also been referred to as satisfying the rank condition.

The definition is left–right symmetric, so it makes no difference whether we define UGN in terms of left or right modules; the two definitions are equivalent.