Test modules for flatness

  • Rafail Alizade

    Yaşar University, Izmir, Turkey
  • Yilmaz Durğun

    Universität Zürich, Switzerland


A right RR-module MM is said to be a test module for flatness (shortly: an f-test module) provided for each left RR-module NN, Tor(M,N)=0(M,N)=0 implies NN is flat. f-test modules are flat version of the Whitehead test modules for injectivity defined by Trlifaj. In this paper the properties of f-test modules are investigated and are used to characterize various families of rings. The structure of a ring over which every (finitely generated) right RR-module is flat or f-test is investigated. Abelian groups that are Whitehead test modules for injectivity or f-test are characterized.

Cite this article

Rafail Alizade, Yilmaz Durğun, Test modules for flatness. Rend. Sem. Mat. Univ. Padova 137 (2017), pp. 75–91

DOI 10.4171/RSMUP/137-4