When an $\mathscr{S}$-closed submodule is a direct summand

Yongduo Wang; Dejun Wu

doi:10.4134/BKMS.2014.51.3.613

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(3): 613-619

Printed May 31, 2014

https://doi.org/10.4134/BKMS.2014.51.3.613

When an $\mathscr{S}$-closed submodule is a direct summand

Yongduo Wang and Dejun Wu

Lanzhou University of Technology, Lanzhou University of Technology

Abstract

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Abstract

It is well known that a direct sum of CLS-modules is not, in general, a CLS-module. It is proved that if $M=M_1\oplus M_2$, where $M_1$ and $M_2$ are CLS-modules such that $M_1$ and $M_2$ are relatively ojective (or $M_1$ is $M_2$-ejective), then $M$ is a CLS-module and some known results are generalized.

Keywords: CLS-module, ejective module, ojective module

MSC numbers: 16D10