Modern Algebra (math 210) Midterm Solutions
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This solution set was written by Pokman; Ravi has added some comments and hopefully hasn’t introduced too many errors! 1. Show that a ring in which all ideals are finitely generated cannot have an infinite sequence of ideals Conversely, show that if a ring has no infinite sequence of ideals, then all ideals are finitely generated. Solution. Suppose all ideals of a ring are finitely generated, and we have an increasing sequence of ideals, The union
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