An irreducible variety is a nonempty algebraic variety that cannot be written as the union of two
proper closed algebraic subsets.
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 VarietyPortions of this entry contributed by Todd Rowland
Explore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Irreducible Variety." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IrreducibleVariety.html