A right -module is said to be a test module for flatness (shortly: an f-test module) provided for each left -module , Tor implies 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 -module is flat or f-test is investigated. Abelian groups that are Whitehead test modules for injectivity or f-test are characterized.
DOI :
10.4171/RSMUP/137-4
Classification :
16, 18
Mots-clés : Whitehead test modules, f-test modules, $p$-indigent modules, flat modules, fully saturated rings
Mots-clés : Whitehead test modules, f-test modules, $p$-indigent modules, flat modules, fully saturated rings
Affiliations des auteurs :
Alizade, Rafail 1 ;
Durğun, Yilmaz 2
@article{RSMUP_2017__137__75_0, author = {Alizade, Rafail and Dur\u{g}un, Yilmaz}, title = {Test modules for flatness}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, pages = {75--91}, publisher = {European Mathematical Society Publishing House}, address = {Zuerich, Switzerland}, volume = {137}, year = {2017}, doi = {10.4171/RSMUP/137-4}, mrnumber = {3652869}, zbl = {1382.16002}, url = {http://www.numdam.org/articles/10.4171/RSMUP/137-4/} }
TY - JOUR AU - Alizade, Rafail AU - Durğun, Yilmaz TI - Test modules for flatness JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2017 SP - 75 EP - 91 VL - 137 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/137-4/ DO - 10.4171/RSMUP/137-4 ID - RSMUP_2017__137__75_0 ER -
%0 Journal Article %A Alizade, Rafail %A Durğun, Yilmaz %T Test modules for flatness %J Rendiconti del Seminario Matematico della Università di Padova %D 2017 %P 75-91 %V 137 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/137-4/ %R 10.4171/RSMUP/137-4 %F RSMUP_2017__137__75_0
Alizade, Rafail; Durğun, Yilmaz. Test modules for flatness. Rendiconti del Seminario Matematico della Università di Padova, Tome 137 (2017), pp. 75-91. doi : 10.4171/RSMUP/137-4. http://www.numdam.org/articles/10.4171/RSMUP/137-4/
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