MATHEMATICA BOHEMICA, Vol. 132, No. 1, pp. 87-96 (2007)

Ring-like structures derived from $\lambda $-lattices
with antitone involutions

Ivan Chajda

Ivan Chajda, Department of Algebra and Geometry, Palacky University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail:

Abstract: Using the concept of the $\lambda $-lattice introduced recently by V. Snasel we define $\lambda $-lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.

Keywords: $\lambda $-lattice, $\lambda $-semilattice, ortholattice, $\lambda $-ortholattice, antitone involution, Boolean quasiring

Classification (MSC2000): 06C15, 16Y99, 06B99, 81P10, 06A12

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