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Algebraic

Meanings and phrases

algebraic

Pronunciation American British Australian Indian
adj.
  1. of or relating to algebra; algebraical

algebraic language

Pronunciation American British Australian Indian
n.
  1. an algorithmic language having statements that resemble algebraic expressions

algebraic number

Pronunciation American British Australian Indian
n.
  1. root of an algebraic equation with rational coefficients
E.g.
  • Also, any constructible number is an algebraic number.
  • The golden ratio is also an algebraic number and even an algebraic integer.
  • Global fields are in the limelight in algebraic number theory and arithmetic geometry.

algebraic geometry

Pronunciation American British Australian Indian
E.g.
  • This result was his first work in algebraic geometry.
  • His main research was in algebraic geometry.
  • See also: derived algebraic geometry.

algebraic topology

Pronunciation American British Australian Indian
E.g.
  • In the 1930s, analysis situs became algebraic topology.
  • This fundamental idea first surfaced in algebraic topology.
  • He studied with Morrel H. Cohen, with a Ph.D. thesis on algebraic topology (1956).

algebraic group

Pronunciation American British Australian Indian
E.g.
  • Hence, formula_51 is a linear algebraic group over "k".
  • Conversely for any root datum there is a reductive algebraic group.
  • Suppose that "G" is an algebraic group defined over a field "k", such as the reals.

algebraic variety

Pronunciation American British Australian Indian
E.g.
  • It is analogous to the included concept of real or complex algebraic variety.
  • The term "variety of algebras" should not be confused with "algebraic variety".
  • The dimension of an algebraic variety may be defined in various equivalent ways.

algebraic structure

Pronunciation American British Australian Indian
E.g.
  • This shows that the order on R is determined by its algebraic structure.
  • The endomorphisms of a nonabelian group generate an algebraic structure known as a near-ring.
  • The purpose of defining a group homomorphism is to create functions that preserve the algebraic structure.

algebraic varieties

Pronunciation American British Australian Indian
E.g.
  • Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties.
  • Real algebraic geometry is the study of the real points of algebraic varieties.
  • Most remarkably, in late 1950s, algebraic varieties were subsumed into Alexander Grothendieck's concept of a scheme.
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