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MATHEMATICA BOHEMICA, Vol. 132, No. 4, pp. 407-422 (2007)
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Directoids with sectionally antitone involutions and skew MV-algebras

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I. Chajda, M. Kolarik

* I. Chajda*, * M. Kolarik*, Department of Algebra and Geometry, Palacky University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mails: ` chajda@inf.upol.cz`, ` kolarik@inf.upol.cz`

**Abstract:** 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. Jezek 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.

**Keywords:** directoid, antitone involution, sectionally switching mapping, MV-algebra, NMV-algebra, WMV-algebra, skew MV-algebra, implication algebra

**Classification (MSC2000):** 06A12, 03G25, 08A05

**Full text of the article:**

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