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Article

Chajda, Ivan
Directoids with sectionally switching involutions. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 45 (2006), issue 1, pp. 35-41
MSC: 03G25, 06A11, 06A12 | MR 2321295 | Zbl 1123.06001
Keywords:
Directoid; commutative directoid; semilattice; involution; implication algebra; sectionally switching mapping
Summary:
It is shown that every directoid equipped with sectionally switching mappings can be represented as a certain implication algebra. Moreover, if the directoid is also commutative, the corresponding implication algebra is defined by four simple identities.
References:
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[2] Chajda I.: Lattices and semilattices having an antitone involution in every upper interval. Comment. Math. Univ. Carol. 44 (2003), 577–585. MR 2062874 | Zbl 1101.06003
[3] Chajda I., Halaš R., Kühr J.: Distributive lattices with sectionally antitone involutions. Acta Sci. Math. (Szeged), 71 (2005), 19–33. MR 2160352 | Zbl 1099.06006
[4] Ježek J., Quackenbush R.: Directoids: algebraic models of up-directed sets. Algebra Universalis 27 (1990), 49–69. MR 1025835
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