$\sigma$-filters of distributive lattices
M. Sambasiva Rao · Discussiones Mathematicae - General Algebra and Applications · 2024
The concept of σ-filters is introduced in distributive lattices and studied some properties of these classes of filters.Two sets of equivalent conditions are derived one for every µ-filter to become a σ-filter and the other for every filter to become a σ-filter of a distributive lattice.A one-to-one correspondence is established between the set of all prime σ-filters of a distributive lattice and the set of all prime σ-filters of its quotient lattice with respect to a congruence.