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f09_mthsc852_midterm1

# f09_mthsc852_midterm1 - MTHSC 852 Midterm 1 Fall 2009...

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MTHSC 852, Midterm 1 Fall 2009 Instructor: Dr. Matthew Macauley Thursday, September 24, 2009 Name Instructions Exam time is 75 minutes You may not use notes or books. PLEASE WRITE NEATLY AND COMPLETELY! Work out what you want to say on scratch paper before you write it out on the test. There are two pages of scratch paper at the end. If you have any doubt about what results you may assume, then ask . Question Points Earned Maximum Points 1 20 2 20 3 20 4 20 5 20 Total 100

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1. (a) Carefully and fully define the following terms (listed in alphabetical order): (i) Com- mutative Ring, (ii) Euclidean Domain, (iii) Field, (iv) Integral Domain, (v) Principal Ideal Domain, (vi) Unique Factorization Domain (b) Order the above six classes of rings by size, e.g., by filling in the following: .
(c) For each proper inclusion, give an explicit example of a ring that is in the larger class but not in the smaller class. (d) Define what it means for a commutative ring to be Noetherian, and add it to (actually, “off of”) the chain in Part (b) in its proper place.

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f09_mthsc852_midterm1 - MTHSC 852 Midterm 1 Fall 2009...

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