On duality between order and algebraic structures in Boolean systems

nski Abstract: We present an extension of the known one-to-one corre- spondence between Boolean algebras and Boolean rings with unit being two types of Boolean systems endowed with order and algebraic struc- tures, respectively. Two equivalent generalizations of Boolean algebras are discussed. We show that there is a one-to-one correspondence between any of the two mentioned generalized Boolean algebras and Boolean rings without unit.