Geodesic
Quasi-valuation maps based on positive implicative ideals in BCK-algebras
Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 65-75

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The notion of PI-quasi-valuation maps of a BCK-algebra is introduced, and related properties are investigated. The relationship between an I-quasi-valuation map and a PI-quasi-valuation map is examined. Conditions for an I-quasi-valuation map to be a PI-quasi-valuation map are provided, and conditions for a real-valued function on a BCK-algebra to be a quasi-valuation map based on a positive implicative ideal are founded. The extension property for a PI-quasi-valuation map is established.
Keywords: (positive implicative) ideal
Mots-clés : S-quasi-valuation map, I-quasi-valuation map, PI-quasi-valuation map. 
@article{ADM_2018_26_1_a6,
     author = {Young Bae Jun and Kyoung Ja Lee and Seok Zun Song},
     title = {Quasi-valuation maps based on positive implicative ideals in {BCK-algebras}},
     journal = {Algebra and discrete mathematics},
     pages = {65--75},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_26_1_a6/}
}
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Young Bae Jun; Kyoung Ja Lee; Seok Zun Song. Quasi-valuation maps based on positive implicative ideals in BCK-algebras. Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 65-75. http://geodesic.mathdoc.fr/item/ADM_2018_26_1_a6/