Hyper L-algebras

In this paper, we introduced the notion of hyper [Formula: see text]-algebras as a generalization of [Formula: see text]-algebras. We studied basic properties of them and investigated the relationship among hyper [Formula: see text]-algebras and some other hyper logical algebras such as hyper ([Formula: see text],BCI) BCK-algebras and hyper hoops. In the following, we defined the notions of (weak) hyper ideals in hyper [Formula: see text]-algebras and then by considering the congruence relation (relative to a hyper ideal) on the hyper [Formula: see text]-algebra, we constructed the quotient hyper [Formula: see text]-algebras and investigated some properties of them.