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On M-operators of q-lattices

100%
Halaš R.
Discussiones Mathematicae - General Algebra and Applications
|
2002
|
tom 22
|
nr 2
119-129
EN
It is well known that every complete lattice can be considered as a complete lattice of closed sets with respect to appropriate closure operator. The theory of q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.
2
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Congruence submodularity

63%
Chajda I., Halaš R.
Discussiones Mathematicae - General Algebra and Applications
|
2002
|
tom 22
|
nr 2
131-139
EN
We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.
3
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Congruences, ideals and annihilators in standard QBCC-algebras

63%
Halaš R., Plojhar L.
Open Mathematics
|
2005
|
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.
4
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On n-normal posets

51%
Halaš R., Joshi V., Kharat V.
Open Mathematics
|
2010
|
tom 8
|
nr 5
985-991
EN
A poset Q is called n-normal, if its every prime ideal contains at most n minimal prime ideals. In this paper, using the prime ideal theorem for finite ideal distributive posets, some properties and characterizations of n-normal posets are obtained.
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