Address:
Corresponding author: M. Sambasiva Rao, Department of Mathematics, MVGR College of Engineering, Vizianagaram, India - 535005
Department of BS& H, Vignan’s Institute of Engineering for Women, Visakhapatnam, Andhra Pradesh, India - 530046
Department of Mathematics, JNTU-K University College of Engineering, Narasaraopeta, India-522616
E-mail:
mssraomaths35@rediffmail.com
phaneendra.arjun@gmail.com
ksobhanjntu@gmail.com
Abstract: The concept of generalized prime $D$-filters is introduced in distributive lattices. Generalized prime $D$-filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime $D$-filters is introduced in distributive lattices and properties of minimal prime $D$-filters are then studied with respect to congruences. Some topological properties of the space of all prime $D$-filters of a distributive lattice are also studied.
AMSclassification: primary 06D99.
Keywords: dense element, filter, D-filter, prime D-filter, congruence, Hausdorff space.
DOI: 10.5817/AM2021-3-157