Let X be a Tychonoff space and C(X), C ( X , ℂ ) be the rings of all real-valued and complex-valued continuous functions defined on X respectively. For each intermediate subring A(X) of C(X), Acharyya and De have introduced the notion of zβA -ideals in A(X) and zβA-filters on β X. For each A(X), we extend this notion to zβA(X)c -ideals and zβA(X)c-filters for an intermediate subring A(X)c of C ( X , ℂ ). We establish a correspondence between the collection of zβA(X)c-ideals in the subrings A(X)c of C ( X , ℂ ) and the collection of zβA(X)c-filters on β X. We study the properties of the zβA(X)c-ideals. We also deduce that the structure space of the subrings A(X)c is homeomorphic to β X.
Jamir et al. (Wed,) studied this question.