Seminar ideas spring 2014. When I taught Commutative Algebra in 2013-2014, we did run a parallel student seminar. Two of the students in the class/seminar wrote PhD dissertations in Algebraic Geometry, two in Commutative Algebra.
Some of my favorite references are:
Bruns and Herzog, "Cohen-Macaulay rings".
Matsumura, "Commutative Algebra".
Matsumura, "Commutative Ring Theory".
My favorite software is Macaulay2. Here is a small Macaulay2 session where I calculated the primary decomposition of an ideal. I used a session like this as I prepared the lecture (in 2013) on primary decomposition. All of the commands I used are explained on-line. I find the
Macaulay2 Table of Contents
to be very helpful.