Consider quasianalytic local rings of germs of smooth functions closed
under composition, implicit equation, and monomial division. We show
that if the Weierstrass Preparation Theorem holds in such a ring then
all elements of it are germs of analytic functions.
26E10 - $C^\infty$-functions, quasi-analytic functions [See also 58C25]
26E05 - Real-analytic functions [See also 32B05, 32C05]
14P15 - Real analytic and semianalytic sets [See also 32B20, 32C05]