6.1, due February 22

Boy, Dr. Jenkins! You weren't kidding when you said that the material was going to take one more step in the abstract direction. The concept of ideals didn't seem too different from that of an equivalence class but as I kept reading I realized that I was confused as to just waht an ideal was.  Because an ideal was initially compared to a modulo n, I immediately thought an ideal was similar to an equivalence class.  Then I read the theorem that showed that I was a subring.  Well equivalence classes aren't rings.  So, since an ideal is a subring, then it must be a set.  But I cannot shake the similarity to an equivalence class.  Am I just getting my wires crossed?