Geodesic
Directoids with sectionally antitone involutions and skew MV-algebras
Mathematica Bohemica, Tome 132 (2007) no. 4, pp. 407-422

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MR Zbl
It is well-known that every MV-algebra is a distributive lattice with respect to the induced order. Replacing this lattice by the so-called directoid (introduced by J. Ježek and R. Quackenbush) we obtain a weaker structure, the so-called skew MV-algebra. The paper is devoted to the axiomatization of skew MV-algebras, their properties and a description of the induced implication algebras.
It is well-known that every MV-algebra is a distributive lattice with respect to the induced order. Replacing this lattice by the so-called directoid (introduced by J. Ježek and R. Quackenbush) we obtain a weaker structure, the so-called skew MV-algebra. The paper is devoted to the axiomatization of skew MV-algebras, their properties and a description of the induced implication algebras.
DOI : 10.21136/MB.2007.133967
Classification : 03G25, 06A12, 06D35, 08A05
Keywords: directoid; antitone involution; sectionally switching mapping; MV-algebra; NMV-algebra; WMV-algebra; skew MV-algebra; implication algebra 
Chajda, I.; Kolařík, M. Directoids with sectionally antitone involutions and skew MV-algebras. Mathematica Bohemica, Tome 132 (2007) no. 4, pp. 407-422. doi: 10.21136/MB.2007.133967
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