Solutions to some problems from Chapter 1 in Atiyah-Macdonald. And more importantly, insights and generalizations

If , where is the Jacobian ideal of a ring , then is a unit for all . looks like a particularly arbitrary expression. Let us break it down. for all is an alternate representation for . All maximal ideals contain . Now let us suppose that is not a unit. Then is contained inContinue reading “Solutions to some problems from Chapter 1 in Atiyah-Macdonald. And more importantly, insights and generalizations”