Ancykutty Joseph, "On incidence algebras and directed graphs", International Journal of Mathematics and Mathematical Sciences, vol. 31, Article ID 206280, 5 pages, 2002. https://doi.org/10.1155/S0161171202007925
On incidence algebras and directed graphs
The incidence algebra of a locally finite poset has been defined and studied by Spiegel and O'Donnell (1997). A poset has a directed graph representing it. Conversely, any directed graph without any cycle, multiple edges, and loops is represented by a partially ordered set . So in this paper, we define an incidence algebra for over , the ring of integers, by where denotes the number of directed paths of length from to and . When is finite of order , is isomorphic to a subring of . Principal ideals of induce the subdigraphs which are the principal ideals of . They generate the ideals of . These results are extended to the incidence algebra of the digraph representing a locally finite weak poset both bounded and unbounded.
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