INTERNATIONAL CONFERENCE ON ALGEBRA IN MEMORY OF KOSTIA BEIDAR
National Cheng Kung University, Tainan March 6–12, 2005
THE EPIMORPHIC PROBLEM FOR CCC(((XXX)))
ROBERT RAPHAEL
MONTREAL, CANADA
We recall that epimorphisms need not be surjective in the category of commutative rings. Assume all spaces Tychonoff. Call a space X ab- solutely CR-epic if whenever X is a subspace of Y the induced ring ho- momorphism from C(Y)to C(X)is a ring epimorphism.
Our goal is characterize absolutely CR-epic spaces. There is an easy description of these spaces in the Lindelof case. There are complete results in the first countable case, and there are nuanced countable examples in the presence of the continuum hypothesis.
The work is joint. The most recent paper is with Barr and Kennison.
![It is rather easy to prove that a non-zero locally nilpotent derivation exists on R only if R is isomorphic toC[t], i.e](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==)