Let R be a ring with additive identity 0. Prove the following:
(a) For all a in R, a(0) = 0.
NOTE: see attached word document for clearer notations.
First 0+0 =0, in any ring;
next, we observe that
a(0 + 0) = a0 = 0
to see this, use the distributive property on the left side to get
a0 + a0 = ...
Properties of a ring with additive identity 0 are proven. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.