A survey of certain algebraic equations in commutative C*-algebras

摘要

Let X be a compact Hausdorff space and C(X) the commutative Banach algebia of all complex-valued continuous functions on X We will consider the following property of C(X) introduced by Karahanjan [13]: For every / C(X) there exist g 6 C(X) and positive integers p, q such that p does not divide q and gp = fq. We will characterize the property above in terms of topology of X We shall also compare the property to square-root closedness, or algebraic closedness of C(X).