Maximal ring of quotients of an incidence algebra. (Q1401624)

Let \(R\) be a commutative ring and \(I(X,R)\) be the incidence algebra of a partially ordered set \(X\) over \(R\). Under some conditions on \(X\), it is proved that the maximal right ring of quotients of \(I(X,R)\) is isomorphic to \(\prod_{s\in S}M_{n_s}(\widehat R)\), where \(\widehat R\) is the maximal right ring of quotients of \(R\), \(S\) is the set of all maximal elements of \(X\), and \(n_s\), \(s\in S\), is the number of elements \(i\in X\) such that \(i\leq s\).