Algebra II

posted by .

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) non-negative 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 -

    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?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 6TH GR. ALGEBRA

    EXTENDING THE LESSON If you add any two rational numbers, the sum is always a rational number. So, the set of rational numbers is closed under addition. Is the set of rational numbers closed under subtraction. multiplication,and division …
  2. Algebra

    I have some understanding of this but not quite sure how to do the problem. Direction & problem below. Direction: Tell whether whole numbers, integers, or rational numbers are the most reasonable to describe each. Explain your answer. …
  3. 9th grade

    Name the set(s) of numbers to which 1.68 belongs. a. rational numbers b. natural numbers, whole numbers, integers, rational numbers c. rational numbers, irrational numbers d. none of the above my answer a)rational numbers
  4. ordered fields

    prove (3x^2 + 4x-1)/(7x^5+5)>0 is field. can you just prove one of the addition axioms?
  5. Math

    Identify all sets to which the number 3 belongs A. Whole numbers, integers, rational numbers B. Rational numbers C. Integers, rational numbers D. Even numbers, whole numbers, integers, rational numbers I THINK IT'S A
  6. Calculus, check my answers, please! 3

    Did I get these practice questions right?
  7. physics

    identify tie force fields from the following : density field, temperatuse field, gravitational field, magnetic field, electrostatic field, electric field
  8. Algebra

    To which subset of real numbers does the following number belong?
  9. Math

    1. Which expression is equivalent to (-2)(a+6)?
  10. 9th grade alebra

    Name the set of numbers to which -10 belongs A whole numbers , integers , rational numbers B rational numbers C integers or rational D whole numbers , natural numbers , integers

More Similar Questions