Quotient structures of BCK/BCI-algebras induced by quasi-valuation maps

Seok-Zun Song (Author), Hashem Bordbar (Author), Young Bae Jun (Author)

Abstract

Relations between I-quasi-valuation maps and ideals in BCK/BCI -algebras are investigated. Using the notion of an I-quasi-valuation map of a BCK/BCI-algebra, the quasi-metric space is induced, and several properties are investigated. Relations between the I-quasi-valuation map and the I-valuation map are considered, and conditions for an I-quasi-valuation map to be an I-valuation map are provided. A congruence relation is introduced by using the I-valuation map, and then the quotient structures are established and related properties are investigated. Isomorphic quotient BCK/BCI-algebras are discussed.

Keywords

ideal;I-quasi-valuation map;I-valuation map;quasi-metric;

Data

Language:	English
Year of publishing:	2018
Typology:	1.01 - Original Scientific Article
Organization:	UNG - University of Nova Gorica
UDC:	51
COBISS:	5491451
ISSN:	2075-1680
Views:	2101
Downloads:	0
Average score:	0 (0 votes)
Metadata:

Other data

URN:	URN:SI:UNG
Type (COBISS):	Not categorized
Pages:	str. 1-11
Volume:	ǂVol. ǂ7
Issue:	ǂiss. ǂ2
Chronology:	2018
DOI:	10.3390/axioms7020026
ID:	11314169