Yes. Linear Algebra, by Hoffman and Kunze. Very rigorous. (detailed proofs).
Edit: I'm sorry, I'm not really sure about what you consider as "Algebra". The book I mentioned is worth for Linear Algebra.
I took algebra a few years back in high school. I understood everything very well and got good grades, but unfortunately my teachers were not so good and stressed memorization over understanding. At this point I am working through Spivak's Calculus and I absolutely love his approach. I was wondering if anyone knew of an algebra analog to this book, something that stresses proofs, because I would like to sharpen my skills and understanding a bit.
"Elementary Linear Algebra, Applied Version" by Anton Howard and Chris Rorres, will be the book for you. It stresses on comprehension (lots of proofs and diagrams to help) and not memorization, which I was faced with once too with my calculus teacher. Hope this helps, and good luck.