DERIVATIONS OF PRIME FILTER THEOREMS GENERATED BY VARIOUS $\cap $-STRUCTURES IN TRANSITIVE $GE$-ALGEBRAS

Author(s):

Sambasiva RAO Mukkamala *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

Properties of prime filters and maximal filters of transitive GE-algebras are investigated. An element-wise characterization is derived for the smallest GE-filter containing a given set. It is proved that the set of all GE-filters of a transitive GE-algebra forms a complete distributive lattice. Four different versions of a prime filter theorem are generalized in transitive GE-algebras. A necessary and sufficient condition is derived for a proper filter of a commutative GE-algebra to become a prime filter.

Keywords:

GE-algebra , GE-filter , prime filter , maximal filter , commutative closed set

Language:
English
Published:
Journal of Algebraic Systems, Volume:12 Issue: 1, Summer-Autumn 2024
Pages:
59 to 78
https://www.magiran.com/p2600808