Geodesic
A Note on Pseudo-Kleene Algebras
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 39-45.

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We introduce the concept of a pseudo-Kleene algebra which is a non-distributive modification of a Kleene algebra introduced by J. A. Kalman [Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485–491.]. Basic properties of pseudo-Kleene algebras are studied. For pseudo-Kleene algebras with a fix-point there are determined subdirectly irreducible members.
Classification : 06B05, 06D30
Keywords: Antitone involution; De Morgan laws; Kleene algebra; distributive lattice; pseudo-Kleene algebra; subdirectly irreducible 
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Chajda, Ivan. A Note on Pseudo-Kleene Algebras. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 39-45. http://geodesic.mathdoc.fr/item/AUPO_2016__55_1_a5/