# Dimension of an algebraic variety

## Measure of a mathematical object studied in the field of algebraic geometry / From Wikipedia, the free encyclopedia

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In mathematics and specifically in algebraic geometry, the **dimension** of an algebraic variety may be defined in various equivalent ways.

Measure of a mathematical object studied in the field of algebraic geometry

Some of these definitions are of geometric nature, while some other are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply also to any algebraic set. Some are intrinsic, as independent of any embedding of the variety into an affine or projective space, while other are related to such an embedding.