Conductor, projectivity and injectivity

Wolmer Vasconcelos

Vol. 46 (1973), No. 2, 603–608

DOI: 10.2140/pjm.1973.46.603

Abstract

Here we discuss the role of the conductor of a ring extension vis-a-vis the descent of projectivity and injectivity. Regarding the former, the first result says that an injective homomorphism of commutative rings descends projectivity if it does so modulo the conductor. The cheap version—that with noetherian hypotheses—of the descent of projectivity by a finite homomorphism due to Gruson then follows easily. A carbon copy—with the natural modification—of the descent of injectivity is also proved.

Mathematical Subject Classification 2000

Primary: 13C10

Milestones

Received: 25 May 1972

Published: 1 June 1973