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Unformatted text preview: Algebra Qualifying Examination January 2002 Directions: 1. Answer all questions. (Total possible is 100 points.) 2. Start each question on a new sheet of paper. 3. Write only on one side of each sheet of paper. Policy on Misprints: The Qualifying Exam Committee tries to proofread the exams as carefully as possible. Nevertheless, the exam may contain a few misprints. If you are convinced a problem has been stated incorrectly, indicate your interpretation in writing your answer. In such cases, do not interpret the problem in such a way that it becomes trivial. Notes: Each ring R referred to in this exam will be assumed to contain a multiplicative identify 1 R . Every left R-module M will have the property that 1 R m = m for all m M , and every homomorphism of rings : R S will be assumed to satisfy the property that (1 R ) = 1 S . is the field of rational numbers, the field of real numbers, the field of complex numbers, the ring of integers, and q a finite field with q elements....
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This note was uploaded on 07/29/2010 for the course MATH 308 taught by Professor Comech during the Spring '08 term at Texas A&M.
- Spring '08