Article

On Modules Which are Isomorphic to Relatively Divisible or Pure Submodules of Each Other

Published in: Quaestiones Mathematicae
Volume 38 , issue 6 , 2015 , pages: 789–792

DOI: 10.2989/16073606.2015.1015650

Author(s): J.E. Macías-Díaz Departamento de Matemáticas y Física, Mexico

Keywords: Primary 13C11 , Secondary 13C60 , 16D50 , Primary 13C11 , Secondary 13C60 , 16D50

Abstract

In this note, we provide a generalization of a well-known result of module theory which states that two injective modules are isomorphic when they are isomorphic to submodules of each other. More precisely, we show here that two RD-injective (respectively, pure-injective) modules over an integral domain are isomorphic if they are isomorphic to relatively divisible (respectively, pure) sub- modules of each other.

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