Witt vectors

[moksih]

Let (a,0,0), (0,b,0) and (0,0,c) three witt vectors of [tex]w_{3}[F_q][/tex].
Calculate their sum, i.e (a,0,0), (0,b,0) and (0,0,c)= ?
Thank you for your help.

[Guest]

(a,0,0) + (0,b,0) + (0,0,c) = (a, b, c)

[moksih]

Thank you for your answer. Would you, please, give me a proof to this identity. In fact, I need a proof or a reference where a an answer with proof of the following question is given :
Let A be a Witt vectors ring such its vectors are o finite length [tex]\ell[/tex] and [tex](a_0, 0,...,0) , (0,a_1,...,0), ..., (0, 0,...,a_{\ell-1})[/tex] are vectors of A. Calculate the sum of those [tex]\ell[/tex] vectors.

[Guest]

How is addition of Witt vectors defined?