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- Title
CONGRUENCES AND BOOLEAN FILTERS OF QUASI-MODULAR p-ALGEBRAS.
- Authors
BADAWY, ABD EL-MOHSEN; SHUM, K. P.
- Abstract
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) ϵ Φ iff x** = y**. Boolean filters [Fa), a ϵ 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 FB(L) = {[Fa) : a ϵ 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 ϵ B(L) are derived. Finally, we consider some properties of congruences with respect to the direct products of Boolean filters.
- Subjects
GEOMETRIC congruences; BOOLEAN algebra; MODULES (Algebra); MATHEMATICAL proofs; MATHEMATICAL bounds
- Publication
Discussiones Mathematicae: General Algebra & Applications, 2014, Vol 34, Issue 1, p109
- ISSN
1509-9415
- Publication type
Article
- DOI
10.7151/dmgaa.1212