Question

Every ring in this test is commutative with 1 and 1 0 1. Which of the followings are prime ideals of Z? (Separate your answers by commas.) A. ( B. (2). C. (9). D. (111). E. (101) 2. Which of the followings are ring homomorphisms? (Separate your answers by commas.) A.φ: Z → Z, defined by (n) =-n for all n E Z B. ф: Z[x] Z, defined by ф(p(z)) p(0) for all p(z) E Z[2] C. : C C. defined by y(z)-z for all z € С, where z is the complex conjugate of z D. φ: С → R. defined by y(z) = V22 for all z є C where z is the complex conjugate of z 3. What are the units of the ring Z18? 4. What are the ideals of the ring Z5? 5. Give an example of a ring R and an ideal I of R such that I is a prime ideal of R but I is not a maximal ideal of R 6. Give an example of a ring that is not an integral domain. 7. Give an example of an integral domain that is not a field

Answer 1

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