# Algebraic

## Meanings and phrases

adj.

- of or relating to algebra; algebraical

n.

- an algorithmic language having statements that resemble algebraic expressions

n.

- root of an algebraic equation with rational coefficients

- 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.

E.g.

- This result was his first work in algebraic geometry.
- His main research was in algebraic geometry.
- See also: derived algebraic geometry.

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).

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.

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.

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.

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.