Annihilator Ideals in Almost Semilattices
Abstract
The concept of annihilator ideal is introduced in an Almost Semi-lattice (ASL) L with 0. It is proved that the set of all annihilator ideals of an ASL L with 0 forms a complete Boolean algebra. The concept of annihilator preserving homomorphism is introduced in an ASL L with 0. A sucient condition for a homomorphism to be annihilator preserving is derived. Finally, it is proved that the homomorphic image and the inverse image of an annihilator
ideal are again annihilator ideals.
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