\(S\)-injective modules. (English) Zbl 1540.16005
Summary: Let \(S\) be a multiplicative subset of a ring \(R\) with unity. A unitary right \(R\)-module \(M\) is referred to as \(S\)-injective if there exist an element \(s \in S\) and an injective \(R\)-submodule \(Q\) of \(M\) such that \(Ms \subseteq Q \subseteq M\). In this paper, we study the structure of \(S\)-injective modules which extend the notion of injective modules. Some characterizations and various examples of \(S\)-injective modules are provided, and the \(S\)-variants of Baer’s criterion, the Bass-Papp theorem, and the Eakin-Nagata-Eisenbud theorem are proven.
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) |
| 16D80 | Other classes of modules and ideals in associative algebras |
| 16P40 | Noetherian rings and modules (associative rings and algebras) |
Keywords:
\(S\)-injective module; injective module; \(S\)-Noetherian ring; bass-papp theorem; Eakin-Nagata-eisenbud theorem; Baer’s criterionReferences:
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