Math 361, Spring 2019, Assignment 7

From cartan.math.umb.edu


Read:

  1. Section 23.

Carefully define the following terms, then give one example and one non-example of each:

  1. f%g (the remainder when f is divided by g).
  2. Root (of a polynomial).
  3. Ideal.
  4. a (the principal ideal generated by a).

Carefully state the following theorems (you need not prove them):

  1. Theorem concerning polynomial long division.
  2. Factor theorem.
  3. Theorem concerning factorization of quadratic and cubic polynomials.
  4. Eisenstein's criterion.
  5. Criterion for a principal ideal to be contained in an arbitrary ideal.
  6. Criterion for a principal ideal to be contained in another principal ideal.
  7. Criterion for two principal ideals to be equal.

Carefully describe the following algorithms:

  1. Sieve of Eratosthenes.

Solve the following problems:

  1. Section 23, problems 1, 3, 9, 11, 12, 13, 14, 18, 19, 20, 21, and 29.


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