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1
Content available remote On homomorphic images and the free distributive lattice extension of a distributive nearlattice
100%
Celani S. , Calomino I.
Reports on Mathematical Logic
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2016
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tom Vol. 51
57--73
EN
In this paper we will introduce N-Vietoris families and prove that homomorphic images of distributive nearlattices are dually characterized by N-Vietoris families. We also show a topological approach of the existence of the free distributive lattice extension of a distributive nearlattice.
2
Content available Prime ideals in the lattice of additive induced-hereditary graph properties
100%
Berger A. , Mihók P.
Discussiones Mathematicae Graph Theory
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2003
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tom 23
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nr 1
117-127
EN
An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove that the prime ideals of the lattice of all additive induced-hereditary properties are divided into two groups, determined either by a set of excluded join-irreducible properties or determined by a set of excluded properties with infinite join-decomposability number. We provide non-trivial examples of each type.
3
Content available Spectra of abelian wekly associative lattice groups
88%
Rachůnek J.
Discussiones Mathematicae - General Algebra and Applications
|
2000
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tom 20
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nr 1
51-61
EN
The notion of a weakly associative lattice group is a generalization of that of a lattice ordered group in which the identities of associativity of the lattice operations join and meet are replaced by the identities of weak associativity. In the paper, the spectral topologies on the sets of straightening ideals (and on some of their subsets) of abelian weakly associative lattice groups are introduced and studied.
4
Content available Balanced d-lattices are complemented
88%
Goldstern M. , Ploščica M.
Discussiones Mathematicae - General Algebra and Applications
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2002
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tom 22
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nr 1
33-37
EN
We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.
5
Content available remote Outer Measures on a Commutative Ring Induced by Measures on Its Spectrum
75%
Dudzik D. , Skrzynski M.
Annales Mathematicae Silesianae
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2017
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tom 31
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nr 1
63-70
EN
On a commutative ring R we study outer measures induced by measures on Spec(R). The focus is on examples of such outer measures and on subsets of R that satisfy the Carathéodory condition.
6
Content available remote Irreducible ideals in BCI-algebras
75%
Huang Y.
Demonstratio Mathematica
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2004
|
tom Vol. 37, nr 1
2--8
EN
In this paper, we show some results of irreducible ideals in BCI-algebras, including that every proper ideal of a BCK-algebra can be decomposed as the intersection of all minimal irreducible ideals associated with it, etc.
7
Content available Representable dually residuated lattice-ordered monoids
75%
Kühr J.
Discussiones Mathematicae - General Algebra and Applications
|
2003
|
tom 23
|
nr 2
115-123
EN
Dually residuated lattice-ordered monoids (DRl-monoids) generalize lattice-ordered groups and include also some algebras related to fuzzy logic (e.g. GMV-algebras and pseudo BL-algebras). In the paper, we give some necessary and sufficient conditions for a DRl-monoid to be representable (i.e. a subdirect product of totally ordered DRl-monoids) and we prove that the class of representable DRl-monoids is a variety.
8
Content available On ternary semifields
75%
Dutta T. , Kar S.
Discussiones Mathematicae - General Algebra and Applications
|
2004
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tom 24
|
nr 2
185-198
EN
In this paper, we introduce the notion of ternary semi-integral domain and ternary semifield and study some of their properties.In particular we also investigate the maximal ideals of the ternary semiring Z¯₀.
9
Content available remote Tychonoff products of two-element sets and some weakenings of the Boolean prime ideal theorem
51%
Keremedis K.
Bulletin of the Polish Academy of Sciences. Mathematics
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2005
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tom Vol. 53, no 4
349-359
EN
Let X be an infinite set, and P(X) the Boolean algebra of subsets of X. We consider the following statements: BPI(X): Every proper filter of P(X) can be extended to an ultrafilter. UF(X): P(X) has a free ultrafilter. We will show in ZF (i.e., Zermelo–Fraenkel set theory without the Axiom of Choice) that the following four statements are equivalent: (i) BPI(ω). (ii) The Tychonoff product 2R, where 2 is the discrete space {0, 1}, is compact. (iii) The Tychonoff product [0, 1] R is compact. (iv) In a Boolean algebra of size ≤ |R| every filter can be extended to an ultrafilter. We will also show that in ZF, UF(R) does not imply BPI(R). Hence, BPI(R) is strictly stronger than UF(R). We do not know if UF(ω) implies BPI(ω) in ZF. Furthermore, we will prove that the axiom of choice for sets of subsets of R does not imply BPI(R) and, in addition, the axiom of choice for well orderable sets of non-empty sets does not imply BPI(ω).
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