Extension of weakly and strongly F-regular rings by flat maps

2002/09/19 by Ian M. Aberbach · 1 citation
Mathematics · #math.AC #msc:13A35

paper · pdf

published as J. Algebra 241 (2001), no. 2, 799--807

arxiv created 2002/09/19 · arxiv updated 2009/11/30

Abstract

Let (R,m) -> (S,n) be a flat local homomorphism of excellent local rings. We investigate the conditions under which the weak or strong F-regularity of R passes to S. We show that is suffices that the closed fiber S/mS be Gorenstein and either F-finite (if R and S have a common test element), or F-rational (otherwise).

Cited by

• F-injectivity does not imply F-fullness in normal domains

Related

• Flat morphisms with regular fibers do not preserve F-rationality
• F-regularity does not deform
• A sufficient condition for strong F-regularity
• Basically regular local homomorphisms
• The F-signature and strong F-regularity