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Article

Chajda, I. ; Kolařík, M.
Directoids with sectionally antitone involutions and skew MV-algebras. (English). Mathematica Bohemica, vol. 132 (2007), issue 4, pp. 407-422
MSC: 03G25, 06A12, 06D35, 08A05 | MR 2365324 | Zbl 1174.06314 | DOI: 10.21136/MB.2007.133967
Keywords:
directoid; antitone involution; sectionally switching mapping; MV-algebra; NMV-algebra; WMV-algebra; skew MV-algebra; implication algebra
Summary:
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.
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