Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

On epimorphisms of non-commutative rings

J. T. Knighta1

a1 Churchill College, Cambridge

From a commutative ring A, Lazard(8) has made a flat injective epimorphism: AB of commutative rings, such that if AC is another flat injective epimorphism of commutative rings, then there is one and only one ring morphism: BC such that the diagram

S030500410007657X_eqnU1

commutes; and he shows too that BC is a flat injective epimorphism. The main aim of the present paper is to make a similar object for not necessarily commutative rings: this is achieved thanks to the notion of an A-prering, intermediate between that of an A-bimodule and that of an A-ring. In passing, prerings are also used to construct a kind of non-commutative ring of fractions.

(Received January 22 1970)

Footnotes

† Died 28 April 1970. Please apply to the Editor of the Proceedings for offprints.