2009/05/06 by N. S. Khripchenko, B. V. Novikov, Boris Novikov · 4 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms
paper · doi:10.1080/00927870802210019
Abstract It is well known that incidence algebras can be defined only for locally finite partially ordered sets (Doubilet et al., Citation1972; Stanley Citation1986). At the same time, for example, the poset of cells of a noncompact cell partition of a topological space is not locally finite. On the other hand, some operations, such as the order sum and the order product (Stanley, Citation1986), do not save the locally finiteness. So it is natural to try to generalize the concept of incidence algebra. In this article, we consider the functions in two variables on an arbitrary poset (finitary series), for which the convolution operation is defined. We obtain the generalization of incidence algebra—finitary 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. Key Words: Incidence algebraPoset2000 Mathematics Subject Classification: Primary 16S60, 16S50Secondary 16G20, 16S34, 16N20 Notes Communicated by I. Shestakov.