Geodesic
Conjugated algebras
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 17-23

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MR Zbl
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.
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.
Classification : 06A12, 06D35, 08A40
Keywords: Conjugated algebras; basic algebra; section antitone involution; quasiorder 
Chajda, Ivan. Conjugated algebras. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 17-23. http://geodesic.mathdoc.fr/item/AUPO_2009_48_1_a1/
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