P. Emanovský, Jiří Rachůnek (2008)
Czechoslovak Mathematical Journal
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Pseudo -autonomous lattices are non-commutative generalizations of -autonomous lattices. It is proved that the class of pseudo -autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo -autonomous lattices can be described as their normal ideals.
Jiří Rachůnek, Zdeněk Svoboda (2014)
Open Mathematics
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Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and...
Rudolf-E. Hoffmann (1982)
Mathematische Zeitschrift
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Ladislav Beran (2004)
Acta Universitatis Carolinae. Mathematica et Physica
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Ján Jakubík (2003)
Czechoslovak Mathematical Journal
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For a pseudo -algebra we denote by the underlying lattice of . In the present paper we investigate the algebraic properties of maximal convex chains in containing the element 0. We generalize a result of Dvurečenskij and Pulmannová.
Ivan Chajda (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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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.