The structure sheaf of an incidence algebra

Abstract

Let R be the incidence algebra of a finite partially ordered set T over a commutative noetherian ring A. Then the spectrum of R is homeomorphic to the product (Spec A) x T, where Spec A has the usual Zariski topology and T has the order topology. An explicit construction is given for the structure sheaf of R over its spectrum.

Rings and sheaves

“…Finally, we also mention the following works: [78,144,160,221,222,240,376,396,397,406,456,465,469,516] biregular if each of its principal ideals is isolated by a direct summand in K (that is, it is generated by a central idempotent) [66];…”