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1
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Prime ideals in the lattice of additive induced-hereditary graph properties

100%
Berger A., Mihók P.
Discussiones Mathematicae Graph Theory
|
2003
|
tom 23
|
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.
2
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Balanced d-lattices are complemented

88%
Goldstern M., Ploščica M.
Discussiones Mathematicae - General Algebra and Applications
|
2002
|
tom 22
|
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.
3
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Spectra of abelian wekly associative lattice groups

88%
Rachůnek J.
Discussiones Mathematicae - General Algebra and Applications
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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
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On ternary semifields

75%
Dutta T., Kar S.
Discussiones Mathematicae - General Algebra and Applications
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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.
5
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Representable dually residuated lattice-ordered monoids

75%
Kühr J.
Discussiones Mathematicae - General Algebra and Applications
|
2003
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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.
6
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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
|
tom 31
|
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.
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