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- W2042601780 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." @default.
- W2042601780 created "2016-06-24" @default.
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- W2042601780 date "2008-06-01" @default.
- W2042601780 modified "2023-10-12" @default.
- W2042601780 title "Extending modules relative to a torsion theory" @default.
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- W2042601780 doi "https://doi.org/10.1007/s10587-008-0022-y" @default.
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