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- 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 numbers12. A field is a fundamental algebraic structure that is widely used in algebra, number theory, and many other areas of mathematics1.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.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.en.wikipedia.org/wiki/Field_(mathematics)Wikipedia definition: 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 do.math.stackexchange.com/questions/2895697/defini…
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ioł 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 similarly as they behave for See more
Historically, three algebraic disciplines led to the concept of a field: the question of solving polynomial equations, algebraic number theory, … See more
Since fields are ubiquitous in mathematics and beyond, several refinements of the concept have been adapted to the needs of particular … See more
Rational numbers
Rational numbers have been widely used a long time before the elaboration of the concept of field. They are numbers that can be written as 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 … 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 Field Theory -- from Wolfram MathWorld
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