Year: 2025
Type: article
Abstract: Moreover, within the realm of field theory, several advanced concepts emerge, such as field automorphisms, which are isomorphism’s from a field to itself preserving the field operations. These automorphisms play a crucial role in Galois theory, providing insights into the structure of field extensions and the solvability of polynomial equations by radicals. Furthermore, the notion of field extensions and their degrees elucidates the relationships between fields, paving the way for deeper explorations into algebraic structures. The algebraic structure of vector spaces and other mathematical objects is defined by the features of the fields that underlie them. The behaviour of vector addition and scalar multiplication is governed by these fields. As a result, fields are an essential part of contemporary algebra and have many applications in many areas of mathematics and beyond. Their mathematical formulation and study include a wide range of notions, from basic qualities to complex theories.
DOI: 10.70388/ijabs250118
Authors: Pooja Pooja, Manjeet singh Jakhar
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4410138726