Explore BrainMass

Explore BrainMass

    Advanced Algebra:commutative ring

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

    Let x and y belong to a commutative ring R with prime characteristic p.

    a) Show that (x + y)^p = x^p + y^p

    b) Show that, for all positive integers n, (x + y)^p^n = x^p^n + y^p^n.

    c) Find elements x and y in a ring of characteristic 4 such that (x + y)^4 != x^4 + y^4.

    © BrainMass Inc. brainmass.com May 20, 2020, 6:58 pm ad1c9bdddf

    Solution Preview

    We know the formula nCk= n! / k! (n-k)!

    a) (x+y)^p = x^p + pC1 x^p-1 y + pC2 x^p-2 y^2 +... + y^p

    In a commutative ring with prime characteristic p all multiples of p are zero
    Since all ...

    Solution Summary

    A commutative ring is contextualized.