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Fixed field

💡 Words with a Similar Meaning to "Fixed field"

Found via reverse dictionary — words that share a conceptual meaning.

WordDefinition
finite fieldnoun(algebra) Synonym of Galois field.
perfect fieldnoun(algebra, field theory) A field K such that every irreducible polynomial over K has distinct roots.
fieldnounA land area free of woodland, cities, and towns; an area of open country.
prime fieldnoun(algebra, field theory) A field that contains no proper subfields.
galois fieldnoun(algebra) A finite field; a field that contains a finite number of elements.
number fieldnoun(algebra, field theory) algebraic number field
subfieldnounA smaller, more specialized area of study or occupation within a larger one
extension fieldnoun(algebra, field theory) A field L which contains a subfield K, called the base field, from which it is generated by adjoining extra elements.
root fieldnoun(algebra, Galois theory) splitting field
field of fractionsnoun(algebra, ring theory) The smallest field in which a given ring can be embedded.
presemifieldnoun(mathematics, algebra) A finite algebra satisfying all the axioms for a skew field except multiplicative associativity and the existence of a multiplicative identity.
splitting fieldnoun(algebra, Galois theory) (of a polynomial) Given a polynomial p over a field K, the smallest extension field L of K such that p, as a polynomial over L, decomposes into linear factors (polynomials of degree 1); (of a set of polynomials) given a set P of polynomials over K, the smallest extension field of K over which every polynomial in P decomposes into linear factors.
algebraic closurenoun(algebra, field theory, of a field F) A field G such that every polynomial over F splits completely over G (i.e., every element of G is a root of some polynomial over F and every root of every polynomial over F is an element of G).
ordered fieldnoun(algebra) A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides.
algebraic number fieldnoun(mathematics, algebraic number theory) A field which includes the rational numbers and has finite dimension as a vector space over the rational numbers.
simple extensionnoun(algebra, field theory) A field extension obtained by adjoining a single element to a given field.
galois extensionnoun(algebra, Galois theory) An algebraic extension that is both a normal and a separable extension; equivalently, an algebraic extension E/F such that the fixed field of its automorphism group (Galois group) Aut(E/F) is the base field F.
field axiomnoun(mathematics) Any of the several axioms that an object should meet to be considered a mathematical field.
primitive elementnoun(algebra, field theory, of a finite field) An element that generates the multiplicative group of a given Galois field (finite field).
field extensionnoun(algebra, field theory, algebraic geometry) Any pair of fields, denoted L/K, such that K is a subfield of L.

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