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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

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.

Congruences, ideals and annihilators in standard QBCC-algebras

63%

Halaš R. , Plojhar L.

Open Mathematics

2005

tom 3

nr 1

83-97

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels.

Congruence submodularity

63%

Chajda I. , Halaš R.

Discussiones Mathematicae - General Algebra and Applications

2002

tom 22

nr 2

131-139

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.

On n-normal posets

51%

Halaš R. , Joshi V. , Kharat V.

Open Mathematics

2010

tom 8

nr 5

985-991

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.