Explore BrainMass

Explore BrainMass

    Proofs with sets

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    (See attached file for full problem description).

    a) Determine the irreducibility of x20-11 over Q(set of rationals), and use it to prove or disprove that the ideal <x20-11> is a maximal ideal of Q[x].
    b) Construct an integral domain R and an element a in R such that a is irreducible but not prime in R.
    c) Suppose that R is a principal ideal domain and a in R is irreducible. If a does not divide b in R, prove that a and b are relatively prime.
    d) Suppose p in N(set of naturals) is a prime number. Show that every element a in Zp has a p-th root, i.e. there is b in Zp with a=bp.

    © BrainMass Inc. brainmass.com October 5, 2022, 5:57 pm ad1c9bdddf


    Solution Summary

    This solution shows how to determine irreducibility and use it in a proof of ideal, construct an integral domain and element with given characteristics, complete a proof that a and b are relatively prime, and complete a proof regarding roots of elements in a group.