MAT-3110 Midterm: MATH 3110 App State Fall2006 Exam2
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Use the backs of the exam pages for scratchwork or for continuation of your answers, if necessary. 2: (20 points): circle true if the statement is always true, possible if the state- ment is true for some examples but false for others, or false if the statement is never true. Then justify your choice! (a) let r be a nite integral domain. True / possible / false: r has no irreducible elements. (b) let r be a unique factorization domain. True / possible / false: r is a euclidean domain. (c) let r be an integral domain, and let p r such that (p) is a prime ideal of r. True / possible / false: p is a prime in r. (d) consider the quotient ring r = z[x]/(x2 + 1). True / possible / false: r has the ascending chain condition. (e) let r be a nite integral domain.
