An algebraic variety is called irreducible if it cannot be written as the union of nonempty algebraic varieties. For example, the set of solutions to is reducible because it is the union of the solutions to and the solutions to .

# Irreducible Variety

## See also

Algebraic Set, Algebraic Variety, Projective Algebraic Variety
*This entry contributed by Todd
Rowland*

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## Cite this as:

Rowland, Todd. "Irreducible Variety." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/IrreducibleVariety.html