Weierstrass preparational theorem for noncommutative rings

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