Test modules for flatness

Alizade, Rafail; Durğun, Yilmaz

doi:10.4171/RSMUP/137-4

Alizade, Rafail ¹ ; Durğun, Yilmaz ²

¹ Yaşar University, IZMIR, TURKEY
² Universität Zürich, ZÜRICH, SWITZERLAND

Rendiconti del Seminario Matematico della Università di Padova, Tome 137 (2017), pp. 75-91.

Résumé

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.

MR Zbl

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

Affiliations des auteurs :

Alizade, Rafail ¹ ; Durğun, Yilmaz ²

¹ Yaşar University, IZMIR, TURKEY
² Universität Zürich, ZÜRICH, SWITZERLAND

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     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/}
}

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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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