We have attempted to explore some cosmological scenarios arising from the field equations with variable  (cosmological constant) taken in a way which conserves the matter tensor. From the field equations and the conservation equation, an equation is obtained in , R, , which points out two trivial solutions: 2 / = 3 with and = 0. The solutions of the field equations have been investigated for  = /R2 where  is a fixed pure number of the order of unity.