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Field (mathematics) - Wikipedia
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 … See more
Informally, a field is a set, along with two operations defined on that set: an addition operation written as a + b, and a multiplication operation written as a ⋅ b, both of which behave … See more
Historically, three algebraic disciplines led to the concept of a field: the question of solving polynomial equations, algebraic number theory, and algebraic geometry. A first step towards the … See more
Since fields are ubiquitous in mathematics and beyond, several refinements of the concept have been adapted to the needs of particular mathematical areas.
Ordered fields
A field F is called an ordered field if any two elements can … See moreFinite fields (also called Galois fields) are fields with finitely many elements, whose number is also referred to as the order of the field. The above introductory example F4 is a field with four … See more
Constructing fields from rings
A commutative ring is a set that is equipped with an addition and multiplication operation and satisfes all the axioms of a field, … See moreWikipedia text under CC-BY-SA license Fields | Brilliant Math & Science Wiki
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