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).

A concise and excellent treatment of what you want can be found in Lang's "Algebra", in the chapter "Matrices and Linear Maps". The tensor product is also given in terms of modules. 
