You probably mean to ask if every ring of finite stable rank has the IBN property. The way the question is written it can be interpreted two ways. Also, the question becomes better if you define some of the terms.
– Dag Oskar MadsenMar 2 '14 at 12:49

Veldkamp claims this (Handbook of incidence geometry, prop. 2.6 pag. 1040). I suppose that his references give a proof.
– user46855Mar 2 '14 at 13:46

Crossposted to math.SE a few days later: math.stackexchange.com/questions/702848/… Talking with the OP, I found out he was interested in rings with stable range $n$ (apparently synonymous with stable rank $n$) for $n>1$. Rings with stable range 1 do indeed have IBN.
– rschwiebMar 25 '14 at 17:48

everyring of finite stable rank has the IBN property. The way the question is written it can be interpreted two ways. Also, the question becomes better if you define some of the terms. – Dag Oskar Madsen Mar 2 '14 at 12:49