Abstract
A ring R with identity element is n-finite if for any pair A, B of n × n matrices over R, AB = In implies BA = In. In module theoretic terms, R is n-finite if and only if in a free R-module of rank n any generating set of n elements is free. If R is n-finite for all positive integers n then R is said to be strongly finite. It is known that all commutative rings, all Artinian rings and all Noetherian rings are strongly finite. These and many other interesting results appear in a paper of P. M. Cohn [1].
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