A reducible variety is an algebraic variety which can be written as the union of two proper closed algebraic subsets. Equivalently,
it has more than one irreducible component. For example, the variety defined by 
is the union of the two coordinate
axes and is therefore reducible.
Reducible Variety
See also
Algebraic Set, Algebraic Variety, Irreducible VarietyExplore with Wolfram|Alpha
References
Hartshorne, R. Algebraic Geometry. New York: Springer-Verlag, 1977.Cite this as:
Weisstein, Eric W. "Reducible Variety." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ReducibleVariety.html