Posted by Sherry on .
Tell whether or not the following sets are fields under the operations + and *. If the set is not a field, tell which one(s) of the Field Axioms do not apply:
a) [rational numbers]
b) [integers]
c) [positive number]
d) nonnegative numbers]
That is a question from my text. Can someone please explain this to me? My teacher said something about 44 examples (because there are 11 field axioms).

Algebra II 
David Q,
Eleven seems rather a lot: according to Wolfram MathWorld (I can't post the address, it seems, but just google "field axioms" to find it) there are five: Associativity, Commutativity, Distributivity, Identity and Inverses. Algebraic definitions of these are given there.
The same site supplies this information about fields: "A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra". Can you apply these to your four sets?