Finitary incidence algebras
  We consider the functions in two variables on an arbitrary poset, for which the convolution operation is defined. We obtain the generalization of incidence algebra and describe its properties: invertibility, the Jackobson radical, idempotents, regular elements. As a consequence a positive solution of the isomorphism problem for such algebras is obtained. 
N. S. Khripchenko, B. V. Novikov