Test modules for flatness


Alizade R. , Durgun Y.

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, cilt.137, ss.75-91, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 137
  • Basım Tarihi: 2017
  • Doi Numarası: 10.4171/rsmup/137-4
  • Dergi Adı: RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
  • Sayfa Sayısı: ss.75-91

Özet

A right R-module M is said to be a test module for flatness (shortly: an f-test module) provided for each left R-module N, Tor(M,N) = 0 implies N is flat. f-test modules are a flat version of the Whitehead test modules for injectivity deflned 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 (flnitely generated) right R-module is flat or f-test is investigated. Abelian groups that are Whitehead test modules for injectivity or f-test are characterized.