On Annihilators in Hoops

초록

We define the notions of annihilators in hoops and study some related attributes of them, and we show that annihilators are ideals of hoop. In addition, we show that all ideals of hoop are a bounded distributive pseudo-complement lattice, and we use this result and demonstrate that the collection of all annihilators of hoop is a Boolean algebra. Also, we use the notion of annihilator and introduce the special kind of ideal of hoop as sigma-ideal and display that all sigma-ideals of hoop are a complete distributive lattice and we consequence that under what condition it is a Boolean algebra.

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