## Cardinality of a linear independent subset of a free module over a commutative ring which is not an integral domain

If R is a commutative ring with unity and not an integral domain and F is a free R-module with rank k,is there a linear independent set with cardinality > k? I prooved that this is not true if R is an integral domain and is true if R is not a commutative ring but i can't see the answer to my question.

-
It's true. Do you know german? matheplanet.com/matheplanet/nuke/html/… – Martin Brandenburg Nov 23 2010 at 9:58
Alternatively (if $k$ is finite): mathlinks.ro/Forum/viewtopic.php?t=124137 – Martin Brandenburg Nov 23 2010 at 10:01
I think this is a multi-dupe: see mathoverflow.net/questions/30860/… and mathoverflow.net/questions/136/… – Kevin Buzzard Nov 23 2010 at 11:00