Is this going by the quarter system or a semester system? I can't imagine doing groups, rings, and fields in a single quarter with significant rigor. That would suck.
Semester system. The first half of the semester would be groups and rings.
I haven't yet seen an algebra class that would start from scratch, define groups and rings for the first time, and do commutative algebra with modules, and fields with Galois theory in a single semester. Usually these take around 2 semesters.