Tuesday, April 22, 14:00, 7.527
Pruefer domains and a fancy basis of the Euclidean square.
In his 1967 thesis, Melvin Hochster characterized the topological spaces
underlying a scheme.
In particular, his criterion yields a very simple characterization of the
subspace of closed (i. e.
visible) points, hence for the maximal ideal space of a commutative ring.
Hochster tried to do the same
for noetherian rings, without success. For special rings like Pruefer or
Bezout domains (arising in
number theory and functional analysis), only partial results could be
obtained. Using an order-theoretic
approach, we give a complete description for the latter two cases. For
example, the unit square
satisfies our criterion, that is, it arises as maximal spectrum of a Pruefer
domain. Topologically, this
means that there exists a special basis of simply connected open sets.