Residuated lattice

Known as: Residuated semilattice 
In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x ≤ y and a monoid x•y which admits operations x… (More)
Wikipedia

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2010
2010
Introduction and summary. In the theory of non-commutative rings certain distinguished subrings, one-sided and two-sided ideals… (More)
  • figure 1
  • figure 3
  • figure 4
Is this relevant?
2010
2010
The reticulation of an algebra was first defined for commutative rings by Simmons [19] and it was extended by Belluce to non… (More)
Is this relevant?
2008
2008
In this paper we define the reticulation of a residuated lattice, prove that it has “good properties“, present two constructions… (More)
Is this relevant?
2004
2004
Dually residuated lattice-ordered monoids (DR`-monoids) generalize lattice-ordered groups and include also some algebras related… (More)
Is this relevant?
Highly Cited
2003
Highly Cited
2003
A residuated lattice is an ordered algebraic structure L = 〈L,∧,∨, · , e, \ , / 〉 such that 〈L,∧,∨〉 is a lattice, 〈L, ·, e〉 is a… (More)
  • figure 1
Is this relevant?
2003
2003
Cancellative residuated lattices are natural generalizations of lattice-ordered groups ( -groups). Although cancellative monoids… (More)
  • figure 1
  • figure 2
  • figure 3
  • figure 4
Is this relevant?
2002
2002
  • Daowen Qiu
  • Science in China Series F: Information Sciences
  • 2002
It reveals some equivalences between automata based on complete residuated lattice-valued logic (calledl valued automata) and the… (More)
Is this relevant?
2002
2002
for a, b, c ∈ L. The class of all commutative residuated lattices, denoted by CRL, is a finitely based variety of algebras… (More)
Is this relevant?
Review
2002
Review
2002
Residuation is a fundamental concept of ordered structures and categories. In this survey we consider the consequences of adding… (More)
  • figure 1
  • figure 2
  • figure 3
  • figure 4
  • figure 5
Is this relevant?
2001
2001
  • Daowen Qiu
  • Science in China Series : Information Sciences
  • 2001
This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it… (More)
Is this relevant?