We introduce the concept of a Brouwerian generalised lattice as an extension of the concept of a Brouwerian lattice. Besides obtaining an equivalent condition for a distributive generalised lattice to be Brouwerian, we obtain some of its properties. Finally, we introduce the notion of the Brouwerian complement of an element in a Brouwerian generalised lattice and discuss some of its properties.

poset, lattice, distributive lattice, Brouwerian lattice