A von Neumann regular extension of a semiprime ring naturally defines a epimorphic extension in the category of rings. These are studied, and four natural examples are considered, two in commutative ring theory, and two in rings of continuous functions.
Theory and Applications of Categories, Vol. 6, 1999, No. 8, pp 94-104 http://www.tac.mta.ca/tac/volumes/6/n8/n8.dvi http://www.tac.mta.ca/tac/volumes/6/n8/n8.ps ftp://ftp.tac.mta.ca/pub/tac/html/volumes/6/n8/n8.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/6/n8/n8.psTAC Home