The Hecke-Kiselman algebra of a finite oriented graph Θ over a field K is studied. If Θ is an oriented cycle, it is shown that the algebra is semiprime and its central localization is a finite direct product of matrix algebras over the field of rational functions K(x). More generally, the radical is described in the case of PI-algebras, and it is shown that it comes from an explicitly described congruence on the underlying Hecke-Kiselman monoid. Moreover, the algebra modulo the radical is again a Hecke-Kiselman algebra and it is a finite module over its center.

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关于Hecke-Kiselman代数的根

研究了场K上有限取向图θ的Hecke-Kiselman代数。如果Θ是有向环，则表明该代数是半素数，并且其中心位置是矩阵代数在有理函数K（x）上的有限直接乘积。更一般而言，在PI代数的情况下描述了部首，并且表明部首来自显式描述的与基础Hecke-Kiselman单面体一致。此外，以基为模的代数再次是Hecke-Kiselman代数，并且是其中心的有限模。