Varieties of commutative integral bounded residuated lattices admitting a Boolean retraction term

DOI10.1007/s11225-012-9453-4zbMath1272.03162OpenAlexW1972460988MaRDI QIDQ1935556

Roberto L. O. Cignoli, Antoni Torrens Torrell

Publication date: 18 February 2013

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11225-012-9453-4

zbMATH Keywords

free algebrasresiduated latticesBoolean productsBoolean retraction term

Mathematics Subject Classification ID

Other algebras related to logic (03G25) Ordered semigroups and monoids (06F05) Free algebras (08B20)

Related Items (14)

Semisimples in varieties of commutative integral bounded residuated lattices ⋮ Frame definability in finitely valued modal logics ⋮ Projectivity and unification in substructural logics of generalized rotations ⋮ A categorical equivalence for Stonean residuated lattices ⋮ Structural and universal completeness in algebra and logic ⋮ Rotation logics ⋮ Lattice-theoretic properties of algebras of logic ⋮ Erratum to: ``Free algebras in varieties of Glivenko MTL-algebras satisfying the equation \({2(x^2) = (2x)^2}\) ⋮ Quasi-discriminator varieties ⋮ Regular elements and Kolmogorov translation in residuated lattices ⋮ Compatibly involutive residuated lattices and the Nelson identity ⋮ On state ideals and state relative annihilators in De Morgan state residuated lattices ⋮ Representation by triples of algebras with an MV-retract ⋮ Projectivity in (bounded) commutative integral residuated lattices

Cites Work

• Indecomposability of free algebras in some subvarieties of residuated lattices and their bounded subreducts
• Residuated lattices. An algebraic glimpse at substructural logics
• Commutative integral bounded residuated lattices with an added involution
• Free algebras in varieties of BL-algebras with a Boolean retract.
• On the structure of hoops
• Boolean products of MV-algebras: hypernormal MV-algebras
• Varieties in which the Pierce stalks are directly indecomposable
• Free algebras in varieties of Glivenko MTL-algebras satisfying the equation \(2(x^{2}) = (2x)^{2}\)
• Free algebras in varieties of Stonean residuated lattices
• Dualities for Equational Classes of Brouwerian Algebras and Heyting Algebras
• Sheaf Constructions and Their Elementary Properties
• Glivenko like theorems in natural expansions of BCK-logic
• Algebras Whose Congruence Lattices are Distributive.
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Varieties of commutative integral bounded residuated lattices admitting a Boolean retraction term