nLab Artin-Tate lemma





(Artin & Tate 1951)
Given a Noetherian commutative ring AA, a commutative algebra BB over AA, and a commutative algebra CC over BB (and thus a commutative algebra over AA), if CC is a finitely generated algebra over AA and CC is a finitely generated module over BB, then BB is a finitely generated algebra over AA. (If AA is a commutative subring of commutative ring BB, then BB is a commutative algebra over AA.)

See also


The original article:


  • Michael Atiyah, Ian G. Macdonald, Introduction to commutative algebra, (1969, 1994) [[pdf, ISBN:9780201407518]]

  • David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Mathematics, 150, Springer-Verlag, 1995, ISBN:0-387-94268-8

Last revised on May 25, 2022 at 06:08:42. See the history of this page for a list of all contributions to it.