Irreducible component

Subset (often algebraic set) that is not the union of subsets of the same nature

In algebraic geometry, an irreducible algebraic set or irreducible variety is an algebraic set that cannot be written as the union of two proper algebraic subsets. An irreducible component of an algebraic set is an algebraic subset that is irreducible and maximal for this property. For example, the set of solutions of the equation xy = 0 is not irreducible, and its irreducible components are the two lines of equations x = 0 and y = 0.

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