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Quotient Hoops Induced by Quasi-Valuation Mapsopen access
- Issue Date
- Oct-2022
- Publisher
- University of Kragujevac, Faculty of Science
- Keywords
- Hoop; S(?)quasi-valuation map; S-? -quasi-valuation map; S?-quasi-valuation map; F-quasi-valuation map; (pseudo) metric space
- Citation
- Kragujevac Journal of Mathematics, v.46, no.5, pp 743 - 757
- Pages
- 15
- Indexed
- SCOPUS
ESCI
- Journal Title
- Kragujevac Journal of Mathematics
- Volume
- 46
- Number
- 5
- Start Page
- 743
- End Page
- 757
- ISSN
- 1450-9628
- Abstract
- In this paper, our aim was making a metric space on hoop algebras, because of that, we introduced the notion of valuation maps from F-quasi-valuation map based on hoops and related properties of them are investigated. By using these notions, we introduced a quasi-metric space. The continuity of operations of a hoop is studied with topology induced by a quasi-valuation. Also, we studied hoop homomorphism and investigated that under which condition this homomorphism is an F-quasi-valuation map. Moreover, we wanted to find a congruence relation on hoops in a new way and study about the quotient structure that is made by it. So, we defined a congruence relation by F-quasi-valuation map and proved that the quotient is a hoop.
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