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 VarietyThis 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