Address: Department of Mathematics, MVGR College of Engineering, Chintalavalasa, Vizianagaram, Andhra Pradesh, India-535005
E-mail: mssraomaths35@rediffmail.com
Abstract: Coherent ideals, strongly coherent ideals, and $\tau $-closed ideals are introduced in pseudo-complemented distributive lattices and their characterization theorems are derived. A set of equivalent conditions is derived for every ideal of a pseudo-complemented distributive lattice to become a coherent ideal. The notion of median prime ideals is introduced and some equivalent conditions are derived for every maximal ideal of a pseudo-complemented distributive lattice to become a median prime ideal which leads to a characterization of Boolean algebras.
AMSclassification: primary 06D99.
Keywords: coherent ideal, strongly coherent ideal, median prime ideal, maximal ideal, Stone lattice, Boolean algebra.
DOI: 10.5817/AM2022-4-213