Annihilator Ideals in Almost Distributive Lattices
G. C. Rao, Mukkamala Sambasiva Rao · 2009
The concept of annihilator ideals is introduced in an Almost Dis-tributive Lattice (ADL)R. It is proved that the set of all annihilator ideals of R forms a complete Boolean algebra. The sufficient condition for R to become a relatively complemented ADL is derived. The con-cept of annihilator preserving homomorphism is introduced in R. A sufficient condition for a homomorphism to be annihilator preserving is derived. Finally, it is proved that the homomorphic images and the inverse images of an annihilator ideal are again annihilator ideals.