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Invariant basis number
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In mathematics, more specifically in the field of ring theory, a ring has the invariant basis number (IBN) property if all finitely generated free left modules over R have a well-defined rank. In the case of fields, the IBN property becomes the statement that finite-dimensional vector spaces have a unique dimension.
Other results
IBN is a necessary (but not sufficient) condition for a ring with no zero divisors to be embeddable in a division ring (confer field of fractions in the commutative case). See also the Ore condition.
Every nontrivial division ring or stably finite ring has invariant basis number.
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