http://www.math.uniri.hr/CroMC2012/abstracts/2/pita_costa_j.pdf
Joao Pita Costa
University of Ljubljana
joaopitacosta@gmail.com
(joint work with Karin Cvetko-Vah)
During the last three decades skew lattices proved to be the most successful
noncommutative generalization of lattices. A skew lattice S is a set S equipped with two associative binary operations ∨ and ∧ that satisfy the absorption laws (b ∧ a) ∨ a = a = a ∨ (a ∧ b) and their duals. Moreover, (S; ∧) and (S; ∨) are regular semigroups of idempotents. The Green’s relation D is a congruence in any skew lattice S decomposing it into maximal rectangular algebras such that S/D is a lattice. Boolean versions of skew lattices have been systematically studied and permit an analogue to the Stone duality.
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