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Congruences and Boolean filters of quasi-modular p-algebras

100%

El-Mohsen Badawy A., Shum K.

Discussiones Mathematicae - General Algebra and Applications

2014

tom 34

nr 1

109-123

The concept of Boolean filters in p-algebras is introduced. Some properties of Boolean filters are studied. It is proved that the class of all Boolean filters BF(L) of a quasi-modular p-algebra L is a bounded distributive lattice. The Glivenko congruence Φ on a p-algebra L is defined by (x,y) ∈ Φ iff x** = y**. Boolean filters [Fₐ), a ∈ B(L) , generated by the Glivenko congruence classes Fₐ (where Fₐ is the congruence class [a]Φ) are described in a quasi-modular p-algebra L. We observe that the set $F_{B}(L) = {[Fₐ): a ∈ B(L)}$ is a Boolean algebra on its own. A one-one correspondence between the Boolean filters of a quasi-modular p-algebra L and the congruences in [Φ,∇] is established. Also some properties of congruences induced by the Boolean filters [Fₐ), a ∈ B(L) are derived. Finally, we consider some properties of congruences with respect to the direct products of Boolean filters.

Filters of lattices with respect to a congruence

100%

Sambasiva Rao M., El-Mohsen Badawy A.

Discussiones Mathematicae - General Algebra and Applications

2014

tom 34

nr 2

213-219

Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of $L_{/θ}$ is obtained.

Ograniczanie wyników

2 Discussiones Mathematicae - General Algebra and Applications

2 El-Mohsen Badawy A.

1 Sambasiva Rao M.

1 Shum K.

2 2014

Wyniki wyszukiwania

Congruences and Boolean filters of quasi-modular p-algebras

Filters of lattices with respect to a congruence