Missouri Journal of Mathematical Sciences

A Note on OI Torsion Abelian Groups

John A. Lewallen and Noel Sagullo

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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

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

First available in Project Euclid: 3 December 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20K10: Torsion groups, primary groups and generalized primary groups
Secondary: 13C05: Structure, classification theorems 13C12: Torsion modules and ideals

OI group OI module OI ring torsion abelian group


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

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