On Baer type criterion for $C$-dense‎, ‎$C$-closed and quasi injectivity

Journal of Linear and Topological Algebra

مقاله 4، دوره 05، شماره 02، مرداد 2016، صفحه 105-109   

نوع مقاله: Research Paper

نویسندگان

H. Barzegar^* ؛ H. Arianpoor

Department of Mathematics, Tafresh University, Tafresh 3951879611, Iran

چکیده

‎For the subclasses $\mathcal{M}_1$ and $\mathcal{M}_2$ of‎ ‎monomorphisms in a concrete category $\mathcal{C}$‎, ‎if $\mathcal‎{M}_2\subseteq \mathcal{M}_1$‎, ‎then $\mathcal{M}_1$-injectivity‎ ‎implies $\mathcal{M}_2$-injectivity‎. ‎The Baer type criterion is about‎ ‎the converse of this fact‎. ‎In this paper‎, ‎we apply injectivity to the classes of $C$-dense‎, ‎$C$-closed‎ ‎monomorphisms‎. ‎The concept of quasi injectivity is also introduced here to‎ ‎investigte the Baer type criterion for these notions‎.

کلیدواژه‌ها

$C$-dense injective‎؛ ‎$C$-closed injective‎؛ ‎quasi-injective

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