P. M. Cohn and Warren Dicks,
Localization in semifirs II.
J. London Math. Soc. (2) 13 (1976), 411-418.
Erratum (February 20, 2004)
In the last line of page 416 and the first line of page 417, it is asserted
that
"R^ is the completion of R with
respect to the powers of m".
However, this is not always true; it fails, for example, if X
is a set given with an
unbounded function X >
{1,2,3,...} and R is k<X>
with the induced grading.
Thus the argument given in the article proves the Inertia Theorem (only)
in the case
where R^ is the completion of R with
respect to the powers of m; this holds,
for example, if R = k<<X>>. For
a correct proof of the general case, see the
proof of Theorem 2.9.15 of
P. M. Cohn, Free rings and their relations, second edition,
Academic Press, London, New York, 1985.
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