Turkish Journal of Mathematics
DOI
10.3906/mat-1502-75
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 $\varepsilon^*$
First Page
397
Last Page
410
Recommended Citation
VAZIRI, YASER; GHADIRI, MANSOUR; and DAVVAZ, BIJAN
(2016)
"The M[--] and --[M] functors and five short lemma in $H_v$-modules,"
Turkish Journal of Mathematics: Vol. 40:
No.
2, Article 14.
https://doi.org/10.3906/mat-1502-75
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss2/14
