A note on pseudo-Kleene algebras. (English) Zbl 1431.06003

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.


06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
06B05 Structure theory of lattices
06D05 Structure and representation theory of distributive lattices


Zbl 0228.06003
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[4] Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485-491. | | · Zbl 0228.06003
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