A family of maximal subalgebras of R. Robinson's algebra

All maximal sub algebras of the algebra of primitive recursive functions $\langle\Phi;+,*,i\rangle$, whose basic sets contain the set
$$A+\{f:f\equiv0\vee(\forall\,x)(x>0\Rightarrow f(x)>0)\}$$
are described. It is shown that they are continuum in number.