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This sentence seems incorrect, if I understand it correctly: "An ideal I of a ring A is irreducible if, and only if.the algebraic set it defines is irreducible (that is, any open subset is dense) for the
Zariski topology, or equivalently if the closed space of spec A consisting of prime ideals
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What is the source of the claim "The converse is not correct, for example the ideal of polynomials in two variables with vanishing terms of first and second order is not irreducible."? --
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containing I is irreducible for the spectral topology." I believe these statements characterize ideals with prime radical, not irreducible ideals.
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is generated by a prime raised to some power and such an element isn't necessarily irreducible. --
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Knowledge. If you would like to participate, please visit the project page, where you can join
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I don't think this (the second part) is true. For example, a primary ideal of
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A quick note to fellow editors (and future me). MathWorld states
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