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Glite Dictionary
🔢 No branching 🌊 Not branched
unramified

unramified

9.9
Having no places where a covering map or field extension branches
  • adjective
  • /ˌʌnˈræmɪfaɪd/
  • Specialized
translation icon : no ramificado
  • An unramified morphism simplifies the analysis of the structure in algebraic geometry.

Examples

  • The mathematician proved that the extension was unramified at all relevant points.

  • In this case, the covering map is unramified, so each fiber has the same number of elements.

  • The function is unramified at that point.

  • An unramified covering map simplifies the analysis.

  • In algebraic geometry, an unramified covering map allows for smooth transitions without any branch points.

  • The concept of unramified extensions simplifies the study of local fields by eliminating complications from local multiplicities.

  • When analyzing morphisms, an unramified one provides clearer insights due to the absence of branching behavior.

Synonyms

unbranched
vsunramified
6.3

Having one main stem and no side growth

is specific to mathematics meaning no branch points or local multiplicity
branchless
vsunramified
4.9

A tree or plant with no branches

is used in mathematics to mean no branch points or multiplicity

Surface Forms

unramified positive

Morphology

unramified = ramified (transparent) = un + ramify + ed

Formed by productive prefixation un- ('not') applied to 'ramified'; the meaning is directly 'not ramified', though the term is technical in mathematics.

Etymology

Unramified combines the prefix un- meaning 'not' with ramify (from Latin ramus) meaning 'branch'. So an unramified extension or map is literally 'not branched' — it has no points where the structure splits, which is why mathematicians use the word for coverings with no branching.