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Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 The concepts of (commutative, transitive, left exchangeable, belligerent, antisymmetric) interior GE‐algebras and bordered interior GE‐algebras are introduced, and their relations and properties are investigated. Many examples are given to support these concepts. A semigroup is formed using the set of interior GE‐algebras.
Jeong-Gon Lee +4 more
wiley +1 more source
Integrally Closed Residuated Lattices [PDF]
Studia Logica, 2019 A residuated lattice is defined to be integrally closed if it satisfies the equations x\x = e and x/x = e. Every integral, cancellative, or divisible residuated lattice is integrally closed, and, conversely, every bounded integrally closed residuated lattice is integral.
José Gil-Férez +2 more
openaire +4 more sources
Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras [PDF]
, 2016 We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering (or directed) unification, that is, the property that for every two unifiers there is a ...
Dzik, Wojciech, Radeleczki, Sándor
core +2 more sources
A Proof of Tarski’s Fixed Point Theorem by Application of Galois Connections [PDF]
, 2014 Two examples of Galois connections and their dual forms are considered. One of them is applied to formulate a criterion when a given subset of a complete lattice forms a complete lattice.
A. Tarski +8 more
core +1 more source
A representation theorem for integral rigs and its applications to residuated lattices [PDF]
, 2015 We prove that every integral rig in Sets is (functorially) the rig of global sections of a sheaf of really local integral rigs. We also show that this representation result may be lifted to residuated integral rigs and then restricted to varieties of ...
Botero, W. J. Zuluaga +2 more
core +3 more sources
Sectionally residuated lattices [PDF]
Miskolc Mathematical Notes, 2005 Summary: The concept of residuum is relativized in the so-called sections of a given lattice. It is shown that such a concept still has a majority of the good properties of residuum. The results correspond to previous ones involved in sectionally pseudocomplemented lattices.
openaire +3 more sources
Left and right compatibility of strict orders with fuzzy tolerance and fuzzy equivalence relations [PDF]
, 2015 The notion of extensionality of a fuzzy relation w.r.t. a fuzzy equivalence was first introduced by Hohle and Blanchard. Belohlavek introduced a similar definition of compatibility of a fuzzy relation w.r.t. a fuzzy equality.
De Baets, Bernard +2 more
core +2 more sources
Singly generated quasivarieties and residuated structures [PDF]
, 2019 A quasivariety K of algebras has the joint embedding property (JEP) iff it is generated by a single algebra A. It is structurally complete iff the free countably generated algebra in K can serve as A.
Anderson A. R. +25 more
core +2 more sources
Residuated Structures Derived from Commutative Idempotent Semirings
Discussiones Mathematicae - General Algebra and Applications, 2019 Since the reduct of every residuated lattice is a semiring, we can ask under what condition a semiring can be converted into a residuated lattice. It turns out that this is possible if the semiring in question is commutative, idempotent, G-simple and ...
Chajda Ivan, Länger Helmut
doaj +1 more source
Hyper Rl-Ideals in Hyper Residuated Lattices
Discussiones Mathematicae - General Algebra and Applications, 2022 In this paper, we introduce the notion of a (strong) hyper RL-ideal in hyper residuated lattices and give some properties and characterizations of them.
Bakhshi Mahmood
doaj +1 more source