Let
R
be a commutative Noetherian ring with identity, and let
M
be a fixed ideal of
R
. Then, trivially, ring multiplication is continuous in the ilf-adic topology. Let S be a multiplicative system in
R
, and let j = j
s
: R → S
-1
R, be the natural map. One can then ask whether (cf. Warner [3, p. 165]) S
-1
R is a topological ring in ihe
j
(
M
)-adic topology. In Proposition 1, I prove this is the case if and only if M ⊂
p
(
S
), where
Hence
S
-1
R
is a topological ring for all
S
if and only if M ⊂ p*(R), where
