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Glite Dictionary
🔢 No branching 🌊 Not branched
unramified

unramified

1 9.9
Having no places where a covering map or field extension branches
  • adjective
  • /ˌʌnˈræmɪfaɪd/
  • Specialized
: 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
1 6.3

Having one main stem and no side growth

is specific to mathematics meaning no branch points or local multiplicity
branchless
vsunramified
1 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.