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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Congruence classes in Brouwerian semilattices

100%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2001
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tom 21
|
nr 2
229-237
EN
Brouwerian semilattices are meet-semilattices with 1 in which every element a has a relative pseudocomplement with respect to every element b, i. e. a greatest element c with a∧c ≤ b. Properties of classes of reflexive and compatible binary relations, especially of congruences of such algebras are described and an abstract characterization of congruence classes via ideals is obtained.
2
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Normal pseudo-BCK-algebras

100%
Dymek G.
Commentationes Mathematicae
|
2011
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tom 51
|
nr 1
EN
A normal pseudo-BCK-algebra \(X\) is an algebra in which every subalgebra of \(X\) is an ideal of \(X\). Characterizations of normal pseudo-BCK-algebras are given.
3
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On maximal ideals of pseudo \(MV\)-algebras

100%
Dymek G., Walendziak A.
Commentationes Mathematicae
|
2007
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tom 47
|
nr 1
EN
We investigate maximal ideals of pseudo MV-algebras and give some characterizations of them. Some properties of a family of maximal ideals of a pseudo MV-algebra generating this algebra are shown as well. Finally, we are interested in finding an example of a pseudo MV-algebra generated by its maximal ideal.
4
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On the intersection graphs of ideals of direct product of rings

88%
Rad N., Jafari S., Ghosh S.
Discussiones Mathematicae - General Algebra and Applications
|
2014
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tom 34
|
nr 2
191-201
EN
In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals of direct product of commutative rings.
5
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Distributive implication groupoids

88%
Chajda I., Halaš R.
Open Mathematics
|
2007
|
tom 5
|
nr 3
484-492
EN
We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.
6
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Erratum to: Congruences and Ideals in a Distributive Lattice with Respect to a Derivation

88%
Barzegar H.
Bulletin of the Section of Logic
|
2019
|
tom 48
|
nr 1
EN
The present note is an Erratum for the two theorems of the paper "Congruences and ideals in a distributive lattice with respect to a derivation" by M. Sambasiva Rao.
7
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Ring-like operations is pseudocomplemented semilattices

75%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2000
|
tom 20
|
nr 1
87-95
EN
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
8
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Direct decompositions of dually residuated lattice-ordered monoids

75%
Rachůnek J., Šalounová D.
Discussiones Mathematicae - General Algebra and Applications
|
2004
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tom 24
|
nr 1
63-74
EN
The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.
9
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Representable dually residuated lattice-ordered monoids

75%
Kühr J.
Discussiones Mathematicae - General Algebra and Applications
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2003
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tom 23
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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.
10
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On Lie algebras of vector fields related to Riemannian foliations

75%
Rybicki T.
Annales Polonici Mathematici
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1993
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tom 58
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nr 2
111-122
EN
Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.
11
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Unconditional convergence in lattice groups with respect to ideals

75%
Boccuto A., Dimitriou X., Papanastassiou N.
Commentationes Mathematicae
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2010
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tom 50
|
nr 2
EN
We deal with unconditional convergence of series and some special classes of subsets of \(\mathbb{N}\).
12
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A note on semidirect sum of Lie algebras

63%
Ostrowski T.
Discussiones Mathematicae - General Algebra and Applications
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2013
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tom 33
|
nr 2
233-247
EN
In the paper there are investigated some properties of Lie algebras, the construction which has a wide range of applications like computer sciences (especially to computer visions), geometry or physics, for example. We concentrate on the semidirect sum of algebras and there are extended some theoretic designs as conditions to be a center, a homomorphism or a derivative. The Killing form of the semidirect sum where the second component is an ideal of the first one is considered as well.
13
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Congruences, ideals and annihilators in standard QBCC-algebras

63%
Halaš R., Plojhar L.
Open Mathematics
|
2005
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tom 3
|
nr 1
83-97
EN
We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels.
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