Relations between L-algebras and other logical algebras

In this paper, by considering the notion of L-algebra, we show that there are relations between L-algebras and some of other logical algebras such as residuated lattices, MTL-algebras, BL-algebras, MV-algebras, BCK-algebras, equality algebras, EQ-algebras and Hilbert algebras. The aim of this paper is to find under what conditions L-algebras are equivalent to these logical algebras.