I’ll preface this post with the fact that I’m assuming a working knowledge of abstract algebra at the undergraduate level, realistically more about definitions than theorems. I’m taking a class this semester on Galois theory and I’ve been occasionally prepping throughout the summer to get back up to speed in various abstract algebra topics. The textbook, Galois Theory (2nd. edition) by Joseph Rotman, is pretty dense compared to what I’m used to; it (reasonably) assumes a familiarity with groups and jumps right into reviewing commutative rings, starting with the definition,