Test modules for flatness


Alizade R., Durgun Y.

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, vol.137, pp.75-91, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 137
  • Publication Date: 2017
  • Doi Number: 10.4171/rsmup/137-4
  • Journal Name: RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.75-91
  • Keywords: Whitehead test modules, f-test modules, p-indigent modules, flat modules, fully saturated rings
  • Çukurova University Affiliated: No

Abstract

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.