Types of Fields
- Finite field
- A field with finitely many elements.
- Ordered field
- A field with a total order compatible with its operations.
- Rational numbers
- Real numbers
- Complex numbers
- Number field
- Finite extension of the field of rational numbers.
- Algebraic numbers
- The field of algebraic numbers is the smallest algebraically closed extension of the field of rational numbers. Their detailed properties are studied in algebraic number theory.
- Quadratic field
- A degree-two extension of the rational numbers.
- Cyclotomic field
- An extension of the rational numbers generated by a root of unity.
- Totally real field
- A number field generated by a root of a polynomial, having all its roots real numbers.
- Formally real field
- Real closed field
- Global field
- A number field or a function field of one variable over a finite field.
- Local field
- A completion of some global field (w.r.t. a prime of the integer ring).
- Complete field
- A field complete w.r.t. to some valuation.
- Pseudo algebraically closed field
- A field in which every variety has a rational point.
- Henselian field
- A field satisfying Hensel lemma w.r.t. some valuation. A generalization of complete fields.
Read more about this topic: Glossary Of Field Theory
Famous quotes containing the words types of, types and/or fields:
“Our children evaluate themselves based on the opinions we have of them. When we use harsh words, biting comments, and a sarcastic tone of voice, we plant the seeds of self-doubt in their developing minds.... Children who receive a steady diet of these types of messages end up feeling powerless, inadequate, and unimportant. They start to believe that they are bad, and that they can never do enough.”
—Stephanie Martson (20th century)
“As for types like my own, obscurely motivated by the conviction that our existence was worthless if we didnt make a turning point of it, we were assigned to the humanities, to poetry, philosophy, paintingthe nursery games of humankind, which had to be left behind when the age of science began. The humanities would be called upon to choose a wallpaper for the crypt, as the end drew near.”
—Saul Bellow (b. 1915)
“When we walk, we naturally go to the fields and woods: what would become of us, if we walked only in a garden or a mall?”
—Henry David Thoreau (18171862)