Weierstrass preparation theorem for noncommutative rings

Abstract

A power series over a complete local ring can be canonically decomposed into the product of an invertible power series and a unital polynomial whose degree coincides with the number of the first invertible coefficient. This statement is known as the Weierstrass preparation theorem. It follows from a more general statement known as the Weierstrass division theorem. The present article contains a detailed proof of generalizations of the Weierstrass preparation theorem and the Weierstrass division theorem for the so-called rings of skew power series. Such rings arise in number theory, and first in studies of formal groups over local fields. Bibliography: 3 titles.