Field or Field - Which is Correct? Ah, the English language, a land of confusion and contradiction. Just when you think you have a grasp on its rules and idiosyncrasies, along comes a pair of words like " field " and "feild" to throw a spanner in the works. So, which one… In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers, and the field of complex numbers. Many other fields, such as fields of rational functions ... FIELD meaning: 1. an area of land, used for growing crops or keeping animals, usually surrounded by a fence: 2. a…. Learn more. In abstract algebra, a field is a type of commutative ring in which every nonzero element has a multiplicative inverse; in other words, a ring \ (F\) is a field if and only if there exists an element \ (e\) such that for every \ (a \in F\), there exists an element \ (a^ {-1} \in F\) such that \ [a \cdot a^ {-1} = a^ {-1} \cdot a = e.\] Fields are useful in forming the scalars in a given vector space; for instance, polynomials can draw coefficients from the field of real numbers, but also may ...
