# $\delta $-ideals in pseudo-complemented distributive lattices

## M. Sambasiva Rao

Address: Department of Mathematics, MVGR College of Engineering, Chintalavalasa, Vizianagaram, Andhra Pradesh, India-535005

E-mail: mssraomaths35@rediffmail.com

Abstract: The concept of $\delta $-ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of $\delta $-ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of $\delta $-ideals. Finally, some properties of $\delta $-ideals are studied with respect to homomorphisms and filter congruences.

AMSclassification: primary 06D99; secondary 06D15.

Keywords: pseudo-complemented distributive lattice, dense element, closed element, \delta -ideal, Stone lattice, congruence.

DOI: 10.5817/AM2012-2-97