MATH 522 Midterm: MATH 522 Louisville Practice Exam 2 150320
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Practice exam #2: fill in the following table. In each cell, place either an x or a checkmark ( ). Place one of these two marks in every cell of the table; empty cells will be automatically incorrect. Unique factorization domain (ufd: let : r r be a surjective ring homomorphism. Prove that if r is a principal ideal domain, then r is also a principal ideal domain. 3. (a) prove that q[x]/ x4 4x3 + 6x 2 is a eld. (b) prove that z5[x]/ x3 + 2x2 + 2x + 2 is a eld. Prove that every ideal in r is nitely generated if and only if r is.
