# Generalized prime $D$-filters of distributive lattices

## A.P. Phaneendra Kumar, M. Sambasiva Rao, and K. Sobhan Babu

Address:

Corresponding author: M. Sambasiva Rao, Department of Mathematics, MVGR College of Engineering, Vizianagaram, India - 535005

Department of BS& H, Vignanâ€™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