Results 1 to 10 of about 157 (130)
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
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
The Relations among Fuzzy t-Filters on Residuated Lattices [PDF]
The Scientific World Journal, 2014 We give the simple general principle of studying the relations among fuzzy t-filters on residuated lattices. Using the general principle, we can easily determine the relations among fuzzy t-filters on different logical algebras.
Huarong Zhang, Qingguo Li
doaj +2 more sources
Classes of Int-Soft Filters in Residuated Lattices [PDF]
The Scientific World Journal, 2014 The notions of int-soft filters, int-soft G-filters, regular int-soft filters, and MV-int-soft filters in residuated lattices are introduced, and their relations, properties, and characterizations are investigated. Conditions for an int-soft filter to be
Young Bae Jun +2 more
doaj +2 more sources
Open Mathematics, 2020 In this paper, by using the ideal theory in residuated lattices, we construct the prime and maximal spectra (Zariski topology), proving that the prime and maximal spectra are compact topological spaces, and in the case of De Morgan residuated lattices ...
Holdon Liviu-Constantin
exaly +3 more sources
The Structure of Semiconic Idempotent Commutative Residuated Lattices
MathematicsIn this paper, we study semiconic idempotent commutative residuated lattices. After giving some properties of such residuated lattices, we obtain a structure theorem for semiconic idempotent commutative residuated lattices. As an application, we make use
Wei Chen
exaly +3 more sources
Characterizations of Some Fuzzy Prefilters (Filters) in EQ-Algebras [PDF]
The Scientific World Journal, 2014 We introduce and study some types of fuzzy prefilters (filters) in EQ-algebras. First, we present several characterizations of fuzzy positive implicative prefilters (filters), fuzzy implicative prefilters (filters), and fuzzy fantastic prefilters ...
Xiao Long Xin +2 more
doaj +2 more sources
The Lattice of Intuitionistic Fuzzy Filters in Residuated Lattices [PDF]
Journal of Applied Mathematics, 2014 The notion of tip-extended pair of intuitionistic fuzzy filters is introduced by which it is proved that the set of all intuitionistic fuzzy filters in a residuated lattice forms a bounded distributive lattice.
Zhen Ming Ma
doaj +3 more sources
On Semitopological De Morgan Residuated Lattices [PDF]
Transactions on Fuzzy Sets and Systems, 2023 The class of De Morgan residuated lattices was introduced by L. C. Holdon (Kybernetika 54(3):443-475, 2018), recently, many mathematicians have studied the theory of ideals or filters in De Morgan residuated lattices and some of them ...
Liviu-Constantin Holdon
doaj +1 more source