The Singular Ideal and the Socle of Incidence Algebras

Let $R$ be a ring with identity and $I(X,R)$ be the incidence algebra of a locally finite partially ordered set $X$ over $R\mathrm{.}$ In this paper, we compute the socle and the singular ideal of the incidence ring for some $X$ in terms of the socle of $R$ and the singular ideal of $R$, respectively.