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Keywords:
$\lambda $-lattice; $\lambda $-semilattice; ortholattice; $\lambda $-ortholattice; antitone involution; Boolean quasiring
$\lambda $-lattice; $\lambda $-semilattice; ortholattice; $\lambda $-ortholattice; antitone involution; Boolean quasiring
Summary:
Using the concept of the $\lambda $-lattice introduced recently by V. Snášel 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.
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