💡 Words with a Similar Meaning to "Fixed field"
Found via reverse dictionary — words that share a conceptual meaning.
| Word | Definition |
|---|---|
| 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. |
| fieldnoun | A 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 |
| subfieldnoun | A 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. |
Translate “Fixed field” into Another Language
Pick a language — the word will be pre-filled in the translator.