- Turkish Journal of Mathematics
- Vol: 40 Issue: 2
- The M[--] and --[M] functors and five short lemma in $H_v$-modules
The M[--] and --[M] functors and five short lemma in $H_v$-modules
Authors : Yaser Vaziri, Mansour Ghadiri, Bijan Davvaz
Pages : 397-410
View : 5 | Download : 3
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :The largest class of multivalued systems satisfying the module-like axioms are the $H_v$-modules. The main tools concerning the class of $H_v$-modules with the ordinary modules are the fundamental relations. Based on the relation $\varepsilon^*$, exact sequences in $H_v$-modules are defined. In this paper, we introduce the $H_v$-module $M[A]$ and determine its heart and the connection between equivalence relations $\varepsilon^*_{M[A]}$ and $\varepsilon^*_A$. Moreover, we define the $M[-]$ and $-[M]$ functors and investigate the exactness and some concepts related to them. Finally, we prove the five short lemma in $H_v$-modules.Keywords : $H_v$-module, exact sequence, five short lemma, weak equality, fundamental relation $varepsilon^*$