Congruences and Boolean filters of quasi-modular p-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 109-123
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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.
Keywords:
p-algebras, quasi-modular p-algebras, Boolean filters, direct products, congruences
@article{DMGAA_2014_34_1_a7,
author = {El-Mohsen Badawy, Abd and Shum, K.},
title = {Congruences and {Boolean} filters of quasi-modular p-algebras},
journal = {Discussiones Mathematicae. General Algebra and Applications},
pages = {109--123},
publisher = {mathdoc},
volume = {34},
number = {1},
year = {2014},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a7/}
}
TY - JOUR AU - El-Mohsen Badawy, Abd AU - Shum, K. TI - Congruences and Boolean filters of quasi-modular p-algebras JO - Discussiones Mathematicae. General Algebra and Applications PY - 2014 SP - 109 EP - 123 VL - 34 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a7/ LA - en ID - DMGAA_2014_34_1_a7 ER -
%0 Journal Article %A El-Mohsen Badawy, Abd %A Shum, K. %T Congruences and Boolean filters of quasi-modular p-algebras %J Discussiones Mathematicae. General Algebra and Applications %D 2014 %P 109-123 %V 34 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a7/ %G en %F DMGAA_2014_34_1_a7
El-Mohsen Badawy, Abd; Shum, K. Congruences and Boolean filters of quasi-modular p-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 109-123. http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a7/