Results 11 to 20 of about 2,056 (173)
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
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Quasicomplemented residuated lattices [PDF]
Soft Computing, 2020 In this paper, the class of quasicomplemented residuated lattices is introduced and investigated, as a subclass of residuated lattices in which any prime filter not containing any dense element is a minimal prime filter. The notion of disjunctive residuated lattices is introduced and it is observed that a residuated lattice is Boolean if and only if it
Saeed Rasouli
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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
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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
n-Normal residuated lattices [PDF]
Soft Computing, 2019 The notion of $n$-normal residuated lattice, as a class of residuated lattices in which every prime filter contains at most $n$ minimal prime filters, is introduced and studied. Before that, the notion of $ $-filter is introduced and it is observed that the set of $ $-filters in a residuated lattice forms a distributive lattice on its own, which ...
Saeed Rasouli, Michiro Kondo
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M‐Hazy Module and Its Homomorphism Theorem
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 Based on a completely distributive lattice M, we propose a new fuzzification approach to a module, which leads to the concept of an M‐hazy module. Different from the traditional fuzzification approach that defines a fuzzy algebra as a fuzzy subset of a classical algebra, we introduce an M‐hazy module by fuzzifications of algebraic operations.
Donghua Huo, Hongyu Liu, Zafar Ullah
wiley +1 more source
The Fuzzy Prime Spectrum of Partially Ordered Sets
International Journal of Mathematics and Mathematical Sciences, Volume 2023, Issue 1, 2023., 2023 We study the space of prime fuzzy ideals (and the space of maximal fuzzy ideals as a subspace) equipped with the hull‐kernel topology in partially ordered sets. Mainly, we investigate the conditions for which the fuzzy prime spectrum of a poset is compact, Hausdorff, and normal, respectively.
Derso Abeje Engidaw +6 more
wiley +1 more source
The prime state ideal theorem in state residuated lattices [PDF]
Categories and General Algebraic Structures with Applications, 2023 The aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice $\mathcal{SI}(L)$ of astate residuated lattice $(L, \varphi)$ andprove that it is a complete Brouwerian lattice ...
Francis Woumfo +2 more
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Some Properties of Weak Γ‐Hyperfilters in OrderedΓ‐Semihypergroups
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 The main purpose of this paper is to study fundamental properties of weak Γ‐hyperfilters on ordered Γ‐semihypergroups that is a generalization of Γ‐hyperfilters. Also, we investigate the relationship between weak Γ‐hyperfilters and prime Γ‐hyperideals in ordered Γ‐semihypergroups.
Yongsheng Rao +4 more
wiley +1 more source