We generalize to an arbitrary variety the von Neumann axiom for a ring. We study its implications on the purity of monomorphisms and the flatness of algebras.
Keywords: variety, flat algebra, pure monomorphism, von Neumann ring, locally finitely presentable category
2000 MSC: 08B30, 18C35, 16E50
Theory and Applications of Categories,
Vol. 13, 2004,
No. 1, pp 5-26.
http://www.tac.mta.ca/tac/volumes/13/1/13-01.dvi
http://www.tac.mta.ca/tac/volumes/13/1/13-01.ps
http://www.tac.mta.ca/tac/volumes/13/1/13-01.pdf