Extensions of Boolean rings and nearrings

In this paper, we introduce the notions of left (right) Boolean rings and nearrings. We give examples to show that left (right) Boolean rings are not commutative in general. We obtain interrelations among these algebraic structures and get conditions under which the structures are commutative. Finally, we study the concept of derivations on left (right) Boolean rings and nearrings and obtain commutativity results.