MATH 205 Midterm: MATH 205 Louisville Exam 2 150306 Solution
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Exam #2 solutions: (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. This justi cation is not necessary when doing the exam, but is included here for your study purposes. In addition, the trivial constant measure assigning measure 0 to every element makes it a euclidean domain, as any division in a eld leaves zero remainder. Z[x] is clearly not a eld, since 2 has no inverse. It is also not a principal ideal domain, since the ideal of polynomials with even constant term, while it is nitely generated as x, 2 , is not generated by a single element of z[x]. Since it is not a principal ideal domain, it cannot be a euclidean domain.
