Ring constructions on finite posets

Christopher Tedd (Manchester)

Frank Adams 1,

In the Noetherian case the problem of finding a (commutative) ring with a given prime spectrum reduces to that of finding a ring whose primes are ordered (under inclusion) in a given way. In particular, given a finite poset X we may construct a ring whose poset of primes is isomorphic to X. In this talk I will describe this construction in detail, indicate how it may be used to represent order-preserving (equivalently, continuous) maps between finite spectra and describe some of the difficulties present in extending to the general Noetherian case. Due to the technical focus of the talk, the mathematics involved will be of a predominantly algebraic/topological nature.

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