## Tsukuba Journal of Mathematics

### On coverings of modules

#### Abstract

Let $R$ be a ring, and let $\tau$ be a torsion theory for R-mod. We give a necessary condition for every R-module to have a $\tau-$torsionfree cover; this necessary condition is close to the known sufficient condition. Then we present a method for computing, $\tau-$torsionfree covers of modules that can be embedded in $Q_{\tau}$-modules where $Q_{\tau}$ is the quotient ring for $\tau$.

#### Article information

Source
Tsukuba J. Math., Volume 24, Number 1 (2000), 15-20.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164042

Digital Object Identifier
doi:10.21099/tkbjm/1496164042

Mathematical Reviews number (MathSciNet)
MR1791327

Zentralblatt MATH identifier
0985.16017

#### Citation

Teply, Mark L.; Rim, Seog Hoon. On coverings of modules. Tsukuba J. Math. 24 (2000), no. 1, 15--20. doi:10.21099/tkbjm/1496164042. https://projecteuclid.org/euclid.tkbjm/1496164042