The Structure of Residuated Lattices
By Kevin Blount, Constantine Tsinakis. International journal of algebra and computation, 2003
336 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/53e53d0090c2d9224fe991e81cd55414002cb523
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Peter Jipsen
- Franco Montagna
- Constantine Tsinakis
- Nikolaos Galatos
- George Metcalfe
- Anatolij Dvurecenskij
- Lavinia Corina Ciungu
In Management Science and Operations Research
- Peter Jipsen
- Franco Montagna
- Constantine Tsinakis
- Nikolaos Galatos
- Anatolij Dvurecenskij
- George Metcalfe
Citations in the corpus
- A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices (2013, neutral): “Proposition 1 (see [3, 8, 10, 11]).”
- A Survey of Residuated Lattices (2002, methodology): “Integral RL IRL FMP[OT99] Decidable FEP [ BvA2 ] Commutative IRL CIRL FMP[OT99] Decidable FEP [BvA1] Cancellative RL CanRL Comm.”
- AMALGAMATION AND INTERPOLATION IN ORDERED ALGEBRAS (2014, background): “It is easily shown (see [5,8]) that the class of pointed residuated lattices forms a congruence distributive variety and that all the preceding conditions may be expressed equationally.”
- Generalized MV-algebras (2005, background): “A lattice-ordered group( -group) is an algebraG = 〈G,∧,∨, ·,−1, e〉 such that 〈G,∧,∨〉 is a lattice,〈G, ·,−1, e〉 is a group, and multiplication is order preserving (or equivalently, it distributes over the lattice operations).”
- Probabilistic Averaging in Bounded Rℓ-Monoids (2006, background): “Recall that normal filters are in a one-to-one correspondence with kernels of homomorphisms of R� -monoids [17, 2 ].”
- The Blok–Ferreirim theorem for normal GBL-algebras and its application (2009, background): “Moreover, all of the above properties can be expressed by equations; cf. [ BT03 , JT02, GO06].”
- Minimal varieties of residuated lattices (2005, background): “Actually, it is also congruence permutable, see [4,12], so it is arithmetical.”
- Residuated frames with applications to decidability (2012, background): “[5] Every residuated lattice is a subalgebra of the nucleus image of the powerset of a monoid.”
- On the structure of generalized BL-algebras (2006, background): “Congruence filters are in one-to-one correspondence with congruence relations on A [5][11], and A is subdirectly irreducible if and only if it has a unique minimal nontrivial congruence filter.”