Abstract
We prove a few results on the sufficiency of generic and codimension-one fibre conditions for determination of the structure of algebras of transcendence degree one. We first show that over a Noetherian normal domain R, a faithfully flat subalgebra of a finitely generated algebra whose generic and codimension-one fibres are A 1 is necessarily the symmetric algebra of an invertible ideal of R. We next prove a structure theorem for a faithfully flat algebra over a locally factorial Krull domain R whose generic and codimension-one fibres are A 1 . For R local, we deduce a minimal sufficient condition for the algebra to be finitely generated and hence A 1 .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
