Hahn series

E159923

Hahn series are formal power series with exponents in an ordered abelian group and well-ordered supports, providing a general framework for constructing large ordered fields that include structures like the surreal numbers.

All labels observed (3)

How this entity was disambiguated

Statements (47)

Predicate Object
instanceOf algebraic structure ⓘ
formal power series ⓘ
mathematical concept ⓘ
ordered field construction ⓘ
appearsIn construction of exponential fields ⓘ
construction of real-closed fields ⓘ
valuation theory of ordered fields ⓘ
componentType coefficients from a base field or ring ⓘ
exponents from an ordered abelian group ⓘ
definedOver ordered abelian group ⓘ
ensuresWellDefinedProductBy well-ordered support condition ⓘ
fieldOfStudy algebra ⓘ
model theory ⓘ
non-Archimedean analysis ⓘ
ordered algebra ⓘ
valuation theory ⓘ
generalizes Laurent series ⓘ
Puiseux series ⓘ
formal power series with integer exponents ⓘ
hasAlternativeName Hahn generalized power series ⓘ
linked to: Hahn series
hasCanonicalValuation support minimum exponent ⓘ
hasConstraintOnSupport every nonempty subset of the support has a least element ⓘ
hasExponentGroup ordered abelian group ⓘ
hasMathematicianNamesake Hans Hahn ⓘ
hasProperty can be equipped with a natural valuation ⓘ
can be made into an ordered field ⓘ
supports transfinite exponents ⓘ
supports well-ordered sets of exponents ⓘ
hasSupportCondition well-ordered support ⓘ
isSpecialCaseOf generalized power series ⓘ
namedAfter Hans Hahn ⓘ
providesFrameworkFor constructing Hahn fields ⓘ
embedding ordered fields ⓘ
relatedConcept Levi-Civita field ⓘ
Malcev–Neumann series ⓘ
linked to: Hahn series

transseries ⓘ
relatedTo surreal numbers ⓘ
supportsOperation Cauchy-type product ⓘ
termwise addition ⓘ
typicalNotation K((G)) for coefficients in K and exponents in G ⓘ
usedIn asymptotic differential algebra ⓘ
construction of saturated valued fields ⓘ
model-theoretic examples of non-Archimedean fields ⓘ
study of ordered exponential fields ⓘ
usedToConstruct large ordered fields ⓘ
maximally valued fields ⓘ
non-Archimedean ordered fields ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Surreal numbers → relatedConcept → Hahn series ⓘ
Hahn series → hasAlternativeName → Hahn generalized power series ⓘ
linked to: Hahn series
Hahn series → relatedConcept → Malcev–Neumann series ⓘ
linked to: Hahn series