Rings whose pure-injective right modules are direct sums of lifting modules
نویسندگان
چکیده
منابع مشابه
Modules whose direct summands are FI-extending
A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$. It is not known whether a direct summand of an FI-extending module is also FI-extending. In this study, it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?
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It is well-known that a countably injective module is Σ-injective. In Proc. Amer. Math. Soc. 316, 10 (2008), 3461-3466, Beidar, Jain and Srivastava extended it and showed that an injective module M is Σ-injective if and only if each essential extension of M(א0) is a direct sum of injective modules. This paper extends and simplifies this result further and shows that an injective module M is Σ-i...
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The pure-injective R-modules are defined easily enough: as those modules which are injective over all pure embeddings, where an embedding A → B is said to be pure if every finite system of R-linear equations with constants from A and a solution in B has a solution in A. But the definition itself gives no indication of the rich theory around purity and pure-injectivity. The purpose of this surve...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2013
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.12.014