Nested Artin strong approximation property

Abstract

Abstract. We study the Artin Approximation property with constraints in a different frame. As a consequence we give a nested Artin Strong Approximation property for algebraic power series rings over a field.

Immediate Extensions of Valuation Rings And

“…The following corollary is a kind of Artin approximation (see [1], [13], [5], [16]) in the frame of valuation rings. Its statement extends the idea of [7,Corollary 8,Theorem 11] and [15,Theorem 14] replacing the order by the valuation.…”

Immediate extensions of valuation rings and ultrapowers

“…The following corollary is a kind of Artin approximation (see [1], [12]) in the frame of valuation rings. Its statement extends the idea of [6,Corollary 8,Theorem 11] and [14,Theorem 14] replacing the order by the valuation.…”