Pacific J. Math.

Addenda

July 12, 2005.

In Section 5, we gave a long proof of

(95): for any ring

Tor

and hence Tor

and deduced

Theorem 5.3: if

Dicks and Schofield, by developing an argument of Dlab and Ringel,

gave a short proof of these facts, and some other results.

These proofs appeared in pages 57-58 of

A. H. Schofield,

LMS Lecture Notes

where credit is very carefully given for everything except (95).

In Example 4.1, we presented a ring of right (and left) global dimension two,

and a (nonfaithful) universal localization thereof of infinite right (and left) global dimension.

We remarked that "no example is known where the global dimension shows a

Twenty-six years later, Theorem 2.1 of

Amnon Neeman, Andrew Ranicki and Aidan Schofield,

Representations of algebras as universal localizations

Math. Proc. Cambridge Philos. Soc.

provided many examples where the global dimension of a (faithful!) universal localization shows

a finite increment.

Incidentally, the authors were unaware of both our example and our remark.

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