Petrillo's recent article in the College Mathematics Journal explained a theorem of Goursat on the subgroups of a direct product of two groups. In this note, we extend this theorem to commutative rings, and to modules over commutative rings and fields.

Author Bio

I grew up on a farm in Northern Alberta, and enrolled in the Bachelor of Science program at the University of Alberta, with a major in Mathematics, and a minor in Biology. In 2008 I transferred to Mount Allison University and will be graduating this spring. In the summer of 2009 I had the opportunity to work with Dr. M. Beattie, under whose guidance I looked at extensions to Goursat's Theorem for Groups. I have long enjoyed playing piano, especially the works of Chopin, and have been an active competitor in track and field. I currently hold the New Brunswick record for women's pentathlon.