Residuated structures and orthomodular lattices
The authors introduce the variety of pointed left-residuated \(\ell\)-groupoids as a common generalization of various classes of residuated structures (e.g., \(\ell\)-groups, Heyting algebras, MV-algebras, De Morgan monoids) and quantum structures (e.g., orthomodular lattices, lattice effect algebras, basic algebras). They study this variety and the lattice of its subvarieties, develop the theory of left nuclei for these structures and extend the theory of join-completions of residuated \(\ell\)-groupoids to the left-residuated case. The latter gives a new proof of MacLaren's theorem for orthomodular lattices.
scientific article; zbMATH DE number 7450670
scientific article