REGULAR FILTERS OF DISTRIBUTIVE LATTICES

Author(s):

Sambasiva Rao Mukkamala * , Phaneendra Kumar Ananthapatnayakuni

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

The concepts of regular filters and π--filters are introduced in distributive lattices. A set of equivalent conditions is given for a D-filter to become a regular filter. For every D-filter, it is proved that there exists a homomorphism whose dense kernel is a regular filter. π--filters are characterized in terms of regular filters and congruences. Some equivalent conditions are given for the space of all prime π-filters to become a Hausdorff space.

Keywords:

Minimal prime D-filter , π-filter , dense element , relatively complemented lattice , Hausdorff space

Language:
English
Published:
Journal of Algebraic Systems, Volume:12 Issue: 2, Winter-Spring 2025
Pages:
283 to 299
https://www.magiran.com/p2637386