MATH 522 Final: MATH 522 Louisville Final 150424 Solution
Document Summary
Exam #2 solutions: (40 points) fill in the following table. In each cell, place either an x or a checkmark. Place a checkmark if a structure of the type named in the row is always a structure of the type named in the column, and an x if not. A unique factorization domain x x x. This justi cation is not necessary when doing the exam, but is included here for your study purposes. An integral domain must be commutative, but it need not have any of the other properties. Z[ 2, 4 2, 8 2, . is a good example of an integral domain which has none of the other listed properties. A principal ideal domain is de nitionally required to be an integral domain (and thus commutative), and every principal ideal domain has been proven to have unique factorization and the ascending chain condition. However, many principal ideal domains, like z or q[x], are not elds.
