Flat cotorsion modules over Noether algebras

  • Ryo Kanda

    Department of Mathematics, Graduate School of Science, Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi, Osaka, 558-8585, Japan
  • Tsutomu Nakamura

    Department of Mathematics, Faculty of Education, Mie University, 1577 Kurimamachiya-cho, Tsu city, Mie, 514-8507, Japan
Flat cotorsion modules over Noether algebras cover
Download PDF

This article is published open access.


For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs' result for a commutative noetherian ring. As a consequence, we show that pointwise Matlis duality gives a bijective correspondence between the isoclasses of indecomposable injective left modules and the isoclasses of indecomposable flat cotorsion right modules. This correspondence is an explicit realization of Herzog's homeomorphism induced from elementary duality of Ziegler spectra.

Cite this article

Ryo Kanda, Tsutomu Nakamura, Flat cotorsion modules over Noether algebras. Doc. Math. 27 (2022), pp. 1101–1167

DOI 10.4171/DM/893