This preview shows page 1. Sign up to view the full content.
Unformatted text preview: R but is not a prime ideal. 6. Section 7.4, Exercise 10: Assume R is commutative. Prove that if P is a prime ideal of R and P contains no zero divisors then R is an integral domain. 7. Section 7.4, Exercise 16: Let x 416 be an element of the polynomial ring E = Z [ x ] and use the bar notation to denote passage to the quotient ring Z [ x ] / ( x 416) . (a) Find a polynomial of degree 3 that is congruent to 7 x 1311 x 9 +5 x 52 x 3 +3 modulo ( x 416) . (b) Prove that x2 and x + 2 are zero divisors in E . 8. Let R be an integral domain with identity. Prove that if R has nitely many elements then R is a eld. 9. Section 7.5, Exercise 4: Prove that any subeld of R must contain Q . 1...
View
Full
Document
This note was uploaded on 01/21/2012 for the course MATH 113 taught by Professor Ogus during the Fall '08 term at University of California, Berkeley.
 Fall '08
 OGUS
 Math, Algebra

Click to edit the document details