Question

Answer b please...

Let R be a ring and let Z(R) := {z ∈ R : zr = rz for all r ∈ R}.

(a) Show that Z(R) ≤ R. It is called the centre of R.

(b) Let R be the quaternions H = {a+bi+cj+dk : a,b,c,d ∈ R} and let S = {a + bi ∈ H}. Show that S is a commutative subring of H, but there are elements in H that do not commute with elements of S.

Answer 1

Hence for p. i in S does not commute with the element q. j in H, for all nonzero real numbers p and q.

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