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Strong NMV-algebras, commutative basic algebras and naBL-algebras

In: Mathematica Slovaca, vol. 63, no. 4
Xiaohong Zhang
Detaily:
Rok, strany: 2013, 661 - 678
Kľúčové slová:
strong \textit{NMV}-algebra, basic algebra, weak \textit{naBL}-algebra, residuated \textit{l}-groupoid, \textit{NMV}-filter
O článku:
The aim of the paper is to investigate the relationship among NMV-algebras, commutative basic algebras and naBL-algebras (i.e., non-associative BL-algebras). First, we introduce the notion of strong NMV-algebra and prove that (1) a strong NMV-algebra is a residuated l-groupoid (i.e., a bounded integral commutative residuated lattice-ordered groupoid); (2) a residuated l-groupoid is commutative basic algebra if and only if it is a strong NMV-algebra. Secondly, we introduce the notion of NMV-filter and prove that a residuated l-groupoid is a strong NMV-algebra (commutative basic algebra) if and only if its every filter is an NMV-filter. Finally, we introduce the notion of weak naBL-algebra, and show that any strong NMV-algebra (commutative basic algebra) is weak naBL-algebra and give some counterexamples.
Ako citovať:
ISO 690:
Zhang, X. 2013. Strong NMV-algebras, commutative basic algebras and naBL-algebras. In Mathematica Slovaca, vol. 63, no.4, pp. 661-678. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0126-1

APA:
Zhang, X. (2013). Strong NMV-algebras, commutative basic algebras and naBL-algebras. Mathematica Slovaca, 63(4), 661-678. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0126-1
O vydaní:
Publikované: 1. 8. 2013