MATH 522 Midterm: MATH 522 Louisville Exam 2 150325
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Exam #2: (20 points) 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. Prove that if p q q is. ) = 0, then p | a0 and q | an. (this result is known as the a fraction in lowest terms such that f ( p. 4. (a) (10 points) prove that z2[x]/ x3 + x2 + 1 is a eld. What is its order? (b) (10 points) prove that z7[x]/ 3x2 + x + 4 is not a eld. Is it an integral domain: (20 points) prove that every prime element of an integral domain is irreducible, (bonus question, 10 extra points) prove that every irreducible element of a principal ideal domain is prime.