Rendiconti del Seminario Matematico della Università di Padova

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Volume 137, 2017, pp. 75–91
DOI: 10.4171/RSMUP/137-4

Test modules for flatness

Rafail Alizade[1] and Yilmaz Durğun[2]

(1) Yaşar University, Izmir, Turkey
(2) Universität Zürich, Switzerland

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 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 $R$-module is flat or f-test is investigated. Abelian groups that are Whitehead test modules for injectivity or f-test are characterized.

Keywords: Whitehead test modules, f-test modules, $p$-indigent modules, flat modules, fully saturated rings

Alizade Rafail, Durğun Yilmaz: Test modules for flatness. Rend. Sem. Mat. Univ. Padova 137 (2017), 75-91. doi: 10.4171/RSMUP/137-4