In this paper we will sharpen
Wiseman’s upper bound on the global dimension of a fibre product [Theorem 2] and
use our bound to compute the global dimension of some examples. Our upper bound
is used to prove a new change of rings theorem [Corollary 4]. Lower bounds on the
global dimension of a fibre product seem more difficult; we obtain a result
[Proposition 12] which allows us to compute lower bounds in some special
cases.