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

Subject Areas : History and biography

H. Barzegar ¹ , H. Arianpoor ²

1 - Department of Mathematics, Tafresh University, Tafresh 3951879611, Iran
2 - Department of Mathematics, Tafresh University, Tafresh 3951879611, Iran

Received: 2016-02-13 Accepted : 2016-09-10 Published : 2016-09-14

Keywords: $C$-dense injective&lrm, , &lrm, $C$-closed injective&lrm, , &lrm, quasi-injective,

Abstract :

‎For the subclasses $\mathcal{M}_1$ and $\mathcal{M}_2$ of‎‎monomorphisms in a concrete category $\mathcal{C}$‎, ‎if $\mathcal‎{M}_2\subseteq \mathcal{M}_1$‎, ‎then $\mathcal{M}_1$-injectivity‎‎implies $\mathcal{M}_2$-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.

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