MAT-4720 Midterm: MATH 4720 App State Fall2010 Test1
Document Summary
Math 4720 & 5210 (pts = 150 + 50) Show your work! and ll out the characteristic for each ring in the nal column. Check the properties which hold for a given ring r. /36 points): if the statement is always true, circle true and prove it. If the statement is never true, circle false and prove that it can never be true. If the statement is true in some cases and false in others, circle possible then give an example and a counter-example. (a) zn[x] is a euclidean domain. True / possible / false: n is prime. (b) (x) r[x] where r is an integral domain. True / possible / false: (x) is not prime. (c) r is an integral domain. f (x) r[x] is a polynomial of degree 1. True / possible / false: f (x) is irreducible. (d) f is a eld.
