Chajda, Ivan A note on pseudo-Kleene algebras. (English) Zbl 1431.06003 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 55, No. 1, 39-45 (2016). Summary: We introduce the concept of a pseudo-Kleene algebra which is a non-distributive modification of a Kleene algebra introduced by J. A. Kalman [Trans. Am. Math. Soc. 87, 485–491 (1958; Zbl 0228.06003)]. Basic properties of pseudo-Kleene algebras are studied. For pseudo-Kleene algebras with a fix-point there are determined subdirectly irreducible members. Cited in 2 Documents MSC: 06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects) 06B05 Structure theory of lattices 06D05 Structure and representation theory of distributive lattices Keywords:antitone involution; De Morgan laws; Kleene algebra; distributive lattice; pseudo-Kleene algebra; subdirectly irreducible Citations:Zbl 0228.06003 PDF BibTeX XML Cite \textit{I. Chajda}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 55, No. 1, 39--45 (2016; Zbl 1431.06003) Full Text: Link OpenURL References: [1] Birkhoff, G.: Lattice Theory. Amer. Math. Soc. Colloqnium Publ. 25, second edition, American Mathematical Society, New York, 1948. | · Zbl 0033.10103 [2] Cignoli, R.: Injective de Morgan and Kleene algebras. Proc. Amer. Math. Soc. 47 (1975), 269-278. | | · Zbl 0301.06009 [3] Crvenkovič, S., Madarasz, R. Sz.: On Kleene algebras. Theoret. Comput. Sci. 108 (1993), 17-24. | | · Zbl 0778.03006 [4] Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485-491. | | · Zbl 0228.06003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.