(Strongly) $M-\pazocal{A}-$Injective(Flat) Modules
Let $M$ be a left $R-$module and $\pazocal{A}=\{A\}_{A\in\pazocal{A}}$ be a family of some submodules of $M$. It is introduced the classes of (strongly) $M-\pazocal{A}-\mathrm{injective}$ and (strongly) $M-\pazocal{A}-\mathrm{flat}$ modules which are denoted by $(S) M-\pazocal{A}I$ and $(S) M-\pazoc...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
29.01.2013
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| Subjects | |
| Online Access | Get full text |
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| Summary: | Let $M$ be a left $R-$module and $\pazocal{A}=\{A\}_{A\in\pazocal{A}}$ be a
family of some submodules of $M$. It is introduced the classes of (strongly)
$M-\pazocal{A}-\mathrm{injective}$ and (strongly) $M-\pazocal{A}-\mathrm{flat}$
modules which are denoted by $(S) M-\pazocal{A}I$ and $(S) M-\pazocal{A}F$,
respectively. It is obtained some characterizations of these classes and the
relationships between these classes. Moreover it is investigated $(S)
M-\pazocal{A}I$ and $(S) M-\pazocal{A}F$ precovers and preenvelopes of modules.
It is also studied $\pazocal{A}$-coherent, $F\pazocal{A}$ and $P\pazocal{A}$
modules. Finally more generally we give the characterization of
$S-\pazocal{A}I(F)$ modules where $\pazocal{A}=\{A\}_{A\in\pazocal{A}}$ is a
family of some left $R-$modules. |
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| DOI: | 10.48550/arxiv.1301.7050 |