## Missouri Journal of Mathematical Sciences

### A Note on OI Torsion Abelian Groups

#### Abstract

Let $R$ be a commutative ring with unity and $M_R$ be a nonzero unital right $R$-module. We say that $M$ is an OI $R$-module if for each $x \in R$, $Mx = M$ implies $x$ is invertible in $R$. We give a characterization of OI torsion abelian groups in terms of their direct summands.

#### Article information

Source
Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 33-36.

Dates
First available in Project Euclid: 3 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1449161365

Digital Object Identifier
doi:10.35834/mjms/1449161365

Mathematical Reviews number (MathSciNet)
MR3431113

Zentralblatt MATH identifier
1337.20061

#### Citation

Lewallen, John A.; Sagullo, Noel. A Note on OI Torsion Abelian Groups. Missouri J. Math. Sci. 27 (2015), no. 1, 33--36. doi:10.35834/mjms/1449161365. https://projecteuclid.org/euclid.mjms/1449161365