Irreducible Variety

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 xy=0 is reducible because it is the union of the solutions to x=0 and the solutions to y=0.

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.

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