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

Author(s):

H. Barzegar * , H. Arianpoor

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
‎For the subclasses $mathcal{M}_1$ and $mathcal{M}_2$ of‎ ‎monomorphisms in a concrete category $mathcal{C}$‎, ‎if $mathcal‎{M}_2subseteq mathcal{M}_1$‎, ‎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.
Keywords:

$C$-dense injective‎ , ‎$C$-closed injective‎ , ‎quasi-injective

Language:
English
Published:
Journal of Linear and Topological Algebra, Volume:5 Issue: 2, Spring 2016
Pages:
105 to 109
https://www.magiran.com/p2262363