Open AccessCongruences and d -filters of principal p -algebras
Author(s) -
Abd El-Mohsen Badawy
Publication year - 2016
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2015.04.003
Subject(s) - congruence relation , mathematics , lattice (music) , pure mathematics , characterization (materials science) , bounded function , principal (computer security) , filter (signal processing) , class (philosophy) , algebra over a field , discrete mathematics , mathematical analysis , computer science , artificial intelligence , physics , materials science , acoustics , computer vision , nanotechnology , operating system
The concept of d-filters is introduced in p-algebras. Some properties of d-filters are studied. It is proved that the class Fd(L) of all d-filters of a p-algebra L is a bounded complete lattice. A characterization of d-filters of a principal p-algebra is given. Also many properties of congruences induced by the d-filters are derived. A relationship between the d-filters of a principal p-algebra L and the congruences in [Φ, ∇] is established