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Characterizations of almost injective modules. (English) Zbl 1326.16005

Dougherty, Steven (ed.) et al., Noncommutative rings and their applications. International conference on noncommutative rings and their applications, Université d’Artois, Lens, France, July 1–4, 2013. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1032-2/pbk; 978-1-4704-2264-6/ebook). Contemporary Mathematics 634, 11-17 (2015).
From the introduction: The purpose of this note is to give various conditions that are equivalent to the almost injectivity of an \(R\)-module \(M\) relative to an \(R\)-module \(N\). These conditions give a unified picture of the properties of almost injectivity and can be applied to special cases. These conditions may look technical but when applied to special cases for modules that are indecomposable, uniform, or being their direct sums, yield interesting results.
For the entire collection see [Zbl 1310.16001].

MSC:

16D50 Injective modules, self-injective associative rings
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
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