The poset of prime ideals of a commutative Noetherian ring.

Nic Clarke (University Of Manchester, School of Mathematics)


In the 1950's Kaplansky asked which posets can occur as the spectrum of a commutative Noetherian ring. I will discuss some of the progress made on this and then focus on the related question of when the spectra of two different rings are order isomorphic. In particular I will outline a partial answer to this question when the rings in question are affine domains of dimension two.

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