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Keywords:
Conjugated algebras; basic algebra; section antitone involution; quasiorder
Conjugated algebras; basic algebra; section antitone involution; quasiorder
Summary:
We generalize the correspondence between basic algebras and lattices with section antitone involutions to a more general case where no lattice properties are assumed. These algebras are called conjugated if this correspondence is one-to-one. We get conditions for the conjugary of such algebras and introduce the induced relation. Necessary and sufficient conditions are given to indicated when the induced relation is a quasiorder which has “nice properties", e.g. the unary operations are antitone involutions on the corresponding intervals.
References:
[1] 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
[2] Chajda, I., Emanovský, P.: Bounded lattices with antitone involutions and properties of MV-algebras. Discuss. Math., Gener. Algebra and Appl. 24 (2004), 31–42. MR 2117673 | Zbl 1082.03055
[3] Chajda, I., Halaš, R., Kühr, J.: Semilattice Structures. Heldermann Verlag, Lemgo, 2007. MR 2326262 | Zbl 1117.06001
[4] Chajda, I., Kühr, J.: A non-associative generalization of MV-algebras. Math. Slovaca 57 (2007), 1–12. MR 2357826 | Zbl 1150.06012
[5] Cignoli, R. L. O., D’Ottaviano, M. L., Mundici, D.: Algebraic Foundations of Many-valued Reasoning. Kluwer Acad. Publ., Dordrecht, 2000. MR 1786097
[6] Halaš, R., Plojhar, L.: Weak MV-algebras. Math. Slovaca 58 (2008), 1–10. MR 2399238 | Zbl 1174.06009
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