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Extending modules relative to a torsion theory

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Abstract

An R-module M is said to be an extending module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the concept of a type 2 τ-extending module, where τ is a hereditary torsion theory on Mod-R. An R-module M is called type 2 τ-extending if every type 2 τ-closed submodule of M is a direct summand of M. If τ I is the torsion theory on Mod-R corresponding to an idempotent ideal I of R and M is a type 2 τ I -extending R-module, then the question of whether or not M/MI is an extending R/I-module is investigated. In particular, for the Goldie torsion theory τ G we give an example of a module that is type 2 τ G -extending but not extending.

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  1. Department of Mathematics, Adnan Menderes University, 09100, Aydin, Türkiye

    Semra Doğruöz

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  1. Semra Doğruöz
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Correspondence to Semra Doğruöz.

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Doğruöz, S. Extending modules relative to a torsion theory. Czech Math J 58, 381–393 (2008). https://doi.org/10.1007/s10587-008-0022-y

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  • DOI: https://doi.org/10.1007/s10587-008-0022-y

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