Books for linear algebra over commutative rings I was thinking about reviewing linear algebra to recover many theorems that I can use over commutative rings with unity. But it seems very tedious and I did not want to make any mistakes on these theorems, as I often need to use them. I am wondering if there are good books out there for this purpose and want to know why they are good.
More specifically, I want a good book that discusses (finite size) matrices over ring and their relationships with $R$-module homomorphisms, where $R$ is a ring or commutative ring (with $1$, of course).

J. S. Milne has a lengthy expository note on commutative algebra on his homepage: http://www.jmilne.org/math/xnotes/ca.html.
As the abstract says, this is written on quite a high level, though: 

These notes prove the basic theorems in commutative algebra required for algebraic geometry and algebraic groups. They assume only a knowledge of the algebra usually taught in advanced undergraduate or first-year graduate courses. However, they are quite concise. 

