On one Laurent series ring over an extension of $\mathbb{Q}$

TL;DR

This paper constructs a Laurent series ring over an extension of the rational numbers using Mal'cev-Neumann construction and explores its properties.

Contribution

It introduces a new Laurent series ring over an extended base field of rationals and analyzes its algebraic properties.

Findings

Constructed a Laurent series ring over an extension of $\

Established properties of the constructed ring.

Demonstrated the applicability of Mal'cev-Neumann construction in this context.

Abstract

In this paper, using the general Mal'cev-Neumann construction of Laurent series rings, we construct a Laurent series ring with a base ring which is an extension of the field $\mathbb{Q}$ of rational numbers. Further, we establish some useful properties of such a ring.