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MATH 504
Algebraic Structures and Functions
Richard Hammack
www.people.vcu.edu/rhammack/Math504/
Section 0: Cardinality of Innite Sets
Recall:
Sets X and Y have the same cardinality, written |X | = |Y
Section 3 Solutions
8. Consider the binary structures M2 (R), and R, , and the map : M2 (R) R dened as (A) = det(A).
Is an isomorphism?
Notice that a property of determinants gives (A B) = det(A B) =
Section 4 Solutions
31. An element x of a group G is called idempotent if x x = x. Prove that any group G has exactly one
idempotent element.
Proof. Certainly e is idempotent, because e e = e, so G ha
Section 0 Solutions
Use this solution key as a guide in resolving the problems (if any) you had on your homework. It also
gives an indication of the level of completeness and detail that Ill be lookin
Section 2 Solutions
(2) (a b) c = b c = a
a (b c) = a a = a
Even though weve shown that (a b) c = a (b c), thats no guarantee that the opeation is
associative. We would have to show (x y) z = x (y z)