A Critical Study on Field and Its Applications: Exploring the Different Types and Applications of Fields

Abstract

A field is a non-zero commutativering that contains a multiplicative inverse for every nonzero element, or equivalentlya ring whose nonzero elements form an abeliangroup under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplicationand division satisfying the appropriateabelian group equations and distributivelaw. The most commonly used fields are the field of realnumbers, the field of complex numbers, and the field of rationalnumbers, but there are also finitefields, fields of functions, algebraic number fields, p-adicfields, and so forth.