Results 11 to 20 of about 673,590 (252)
Transactions of the American Mathematical Society, 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, Morgan, Dilworth, R. P.
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On State Ideals and State Relative Annihilators in De Morgan State Residuated Lattices [PDF]
International Journal of Mathematics and Mathematical Sciences, 2022 The concept of state has been considered in commutative and noncommutative logical systems, and their properties are at the center for the development of an algebraic investigation of probabilistic models for those algebras.
Francis Woumfo +3 more
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Fuzzy Prime Ideal Theorem in Residuated Lattices
International Journal of Mathematics and Mathematical Sciences, 2021 This paper mainly focuses on building the fuzzy prime ideal theorem of residuated lattices. Firstly, we introduce the notion of fuzzy ideal generated by a fuzzy subset of a residuated lattice and we give a characterization.
Pierre Carole Kengne +2 more
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On Integral Transforms for Residuated Lattice-Valued Functions [PDF]
Information Processing and Management of Uncertainty in Knowledge-Based Systems18th International Conference, 2020 The article aims to introduce four types of integral transforms for functions whose function values belong to a complete residuated lattice. The integral transforms are defined using so-called qualitative residuum based fuzzy integrals and integral ...
M. Holčapek, V. Bui
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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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Archimedean Residuated Lattices [PDF]
Annals of the Alexandru Ioan Cuza University - Mathematics, 2010 For a residuated lattice A we denote by Ds(A) the lattice of all deductive systems (congruence lters) of A. The aim of this paper is to put in evidence new cha- racterizations for maximal and prime elements of Ds(A) and to characterize archimedean and hyperarchimedean residuated lattices; so we prove some theorems of Nachbin type for residuated ...
Antoneta Jeflea, Dumitru Bus, Dana Piciu
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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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Regular Partial Residuated Lattices and Their Filters [PDF]
Mathematics, 2022 To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based
Nan Sheng, Xiaohong Zhang
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Gődel filters in residuated lattices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper, in the spirit of [4], we study a new type of filters in residuated lattices : Gődel filters. So, we characterize the filters for which the quotient algebra that is constructed via these filters is a Gődel algebra and we establish the ...
Piciu Dana +2 more
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