prime subfield

The prime subfield of a field $F$ is the intersection of all subfields of $F$ , or equivalently the smallest subfield of $F$ . It can also be constructed by taking the quotient field of the additive subgroup of $F$ generated by the multiplicative identity $1$ .

If $F$ has characteristic $p$ where $p>0$ is a prime, then the prime subfield of $F$ is isomorphic to the field $\\mathbb{Z}/p\\mathbb{Z}$ of integers mod $p$ . When $F$ has characteristic zero, the prime subfield of $F$ is isomorphic to the field $\\mathbb{Q}$ of rational numbers.

单词	PrimeSubfield
释义	prime subfield The prime subfield of a field $F$ is the intersection of all subfields of $F$ , or equivalently the smallest subfield of $F$ . It can also be constructed by taking the quotient field of the additive subgroup of $F$ generated by the multiplicative identity $1$ . If $F$ has characteristic $p$ where $p>0$ is a prime, then the prime subfield of $F$ is isomorphic to the field $\\mathbb{Z}/p\\mathbb{Z}$ of integers mod $p$ . When $F$ has characteristic zero, the prime subfield of $F$ is isomorphic to the field $\\mathbb{Q}$ of rational numbers.
随便看	54InductiveTypesAreInitialAlgebras 5.4 Inductive types are initial algebras 55HomotopyinductiveTypes 5.5 Homotopy-inductive types 56TheGeneralSyntaxOfInductiveDefinitions 5.6 The general syntax of inductive definitions 57GeneralizationsOfInductiveTypes 5.7 Generalizations of inductive types 58IdentityTypesAndIdentitySystems 5.8 Identity types and identity systems 5Entanglement 5. Entanglement 5Induction 5. Induction 610Quotients 6.10 Quotients 611Algebra 6.11 Algebra 612TheFlatteningLemma 6.12 The flattening lemma 613TheGeneralSyntaxOfHigherInductiveDefinitions 6.13 The general syntax of higher inductive definitions 61Introduction 6.1 Introduction 62InductionPrinciplesAndDependentPaths