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
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 ...
A commutative ring is contextualized.