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Unformatted text preview: Final Exam Study Sheet April 30, 2010 You will have 10 questions, and 3 hours to complete the exam. If you score is higher on the final exam than you score up to and including the final, then your course grade will be the final exam grade (maximal grading policy). First, look at the study sheets for midterm 1 and midterm 2. In addition to that material, you will be expected to know the materials below. The new stuff is basically some of the material on tensors of a ring with a module, and associate algebras. Know what is meant by S R M , where R is a subring of a ring S . Know what is meant by the rank of an R-module, where R is a PID (actually, you can also do it, more generally, for R an integral domain). Basically, using the Fundamental Theorem of Finitely Generated Mod- ules over a PID, we know that M = M 1 M 2 M k , where the M i are cyclic R-modules (this is a direct sum here)....
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- Spring '10