A note on Jacobsan radicals in special Boolean like rings

In this paper we endure the learning of Special Boolean-like rings(BLR) . In segment 1 we debate the assets of a Special Boolean-like ring. If R is a commutative ring with unity , we verify that R is a Special BLR allowing that R is a BLR. Further we display that a Special BLR is regular ⇔ it is a BR. A method is given to construct special Boolean rings from Boolean rings and certain modules over them. In section 2 we prove that a SBLR ‘ R’ is a subdirect product of a family of rings {R_i}, somewhere individually R_i is either a two component field or a four component BLR H4 or a zero-ring. In section 3 we discussed nearby the Jacobson radical J(R) of a Special BLR, R and demonstrate that J(R)=N( R) , where N(R) is the nilradical of R. As a moment of this, we illustration that every BR is semi simple. Finally we demonstrate that every special BLR which is semisimple, is a BR.