# Thus the decomposition of algebraic sets into irreducible ones corresponds to writing a radical ideal as an intersection of prime ideals

I read this assertion in Irena Swanson's Thesis:$\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$$\qquad$$\qquad$$\qquad$$\qquad$"In the standard correspondence between algebraic sets and ideals, algebraic sets correspond to radical ideals and irreducible algebraic sets correspond to prime ideals. Thus the decomposition of algebraic sets into irreducible ones corresponds to writing a radical ideal as an intersection of prime ideals." Why?

• Do you know what this correspondance between radical ideals and algebraic sets is ? – Captain Lama Apr 17 '16 at 19:19
• And do you know that $V(I\cap J) = V(I)\cup V(J)$ ? – Captain Lama Apr 17 '16 at 19:22
• Yes, I know it. – Ancastack Apr 17 '16 at 19:24