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‎Pure Ideals in Residuated Lattices [PDF]

Transactions on Fuzzy Sets and Systems, 2022
Ideals in MV algebras are‎, ‎by definition‎, ‎kernels of homomorphism‎. ‎An ideal is the dual of a filter in some special logical algebras but not in non-regular residuated lattices‎.
Istrata Mihaela
doaj   +2 more sources

Residuated Lattices. [PDF]

Proc Natl Acad Sci U S A, 1938
Let \(R\) be any commutative ring with unity, and let \(L\) be the lattice of the ideals of \(R\). It is known that \(L\) is a modular lattice. The authors announce further conditions on \(L\); for example, if \(L\) is complemented, then it is a Boolean algebra -- thus it cannot be a non-trivial projective geometry.
Ward M, Dilworth RP.
europepmc   +6 more sources

Nilpotent Elements of Residuated Lattices [PDF]

International Journal of Mathematics and Mathematical Sciences, 2012
Some properties of the nilpotent elements of a residuated lattice are studied. The concept of cyclic residuated lattices is introduced, and some related results are obtained.
Shokoofeh Ghorbani, Lida Torkzadeh
doaj   +2 more sources

The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 2; peer review: 3 approved] [PDF]

F1000Research
This paper introduces the concept of fuzzy filters and 2-fuzzy filters of a quasi-ordered residuated system K . This research explores comparative, normal, implicative and associative fuzzy filters within a quasi-ordered residuated system. It establishes
Teferi Getachew Alemayehu, Yeshiwas Mebrat Gubena   +1 more
doaj   +2 more sources

On residuated n-lattice

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
In this paper, we introduce residuated n-lattice: a variety of residuated semigroup equipped with binary hyperoperations n-sup and n-inf. We define the left bound, right bound, n-supremum, n-infimum, maximum and minimum with respect to it′s relation.
Zahiri Saeide, Saeid Arsham Borumand
doaj   +2 more sources

Some properties of state filters in state residuated lattices [PDF]

Mathematica Bohemica, 2021
We consider properties of state filters of state residuated lattices and prove that for every state filter $F$ of a state residuated lattice $X$: \begin{itemize} \item[(1)] $F$ is obstinate $\Leftrightarrow$ $L/F \cong\{0,1\}$; \item[(2)] $F$ is primary $
Michiro Kondo
doaj   +1 more source

Gluing Residuated Lattices

Order, 2023
This is a preprint.
Nikolaos Galatos, Sara Ugolini
openaire   +3 more sources

Residuated Lattices with Noetherian Spectrum

Mathematics, 2022
In this paper, we characterize residuated lattices for which the topological space of prime ideals is a Noetherian space. The notion of i-Noetherian residuated lattice is introduced and related properties are investigated.
Dana Piciu, Diana Savin
doaj   +1 more source

Residuation in twist products and pseudo-Kleene posets [PDF]

Mathematica Bohemica, 2022
M. Busaniche, R. Cignoli (2014), C. Tsinakis and A. M. Wille (2006) showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations.
Ivan Chajda, Helmut Länger
doaj   +1 more source

Intuitionistic FWI-ideals of residuated lattice Wajsberg algebras

Ratio Mathematica, 2021
The notions of intutionistic fuzzy Wajsberg implicative ideal( –ideal) and intuitionistic fuzzy lattice ideal of residuated Wajsberg algebras are introduced.
Shanmugapriya R. Shanmugapriya, Ibrahim Abdul   +1 more
doaj   +1 more source