In his work on transcendental numbers Edmond Maillet was led to the question whether it is possible to introduce the notion of an "integral element" in the field ℂ of all complex numbers in analogy to the notions of a rational integer (i.e. an integral element in the field ℚ of all rational numbers) and of an algebraic integer (i.e. an integral element in the field A of all algebraic numbers). More precisely, if ℤ = ">I_ℚ is the usual ring of (rational) integers and I_A the usual ring of algebraic integers, Maillet asked whether there exists a ring I_ℂ of complex numbers.