KERNEL IDEALS IN ALMOST DISTRIBUTIVE LATTICES
Mukkamala Sambasiva Rao, G. C. Rao · Asian-European Journal of Mathematics · 2012
The concepts of ⋆-congruences and kernel ideals are introduced in a pseudo-complemented almost distributive lattice (ADL). A necessary and sufficient condition for a congruence to become a ⋆-congruence is derived. Some equivalent conditions for every ideal of a pseudo-complemented ADL to become a kernel ideal are derived. Prime kernel ideals are characterized in terms of minimal prime ideals. Properties of kernel ideals are observed in Stone ADLs.