Finitary Incidence Algebras

被引:31
|
作者
Khripchenko, N. S. [1 ]
Novikov, B. V. [1 ]
机构
[1] Kharkov Natl Univ, Dept Mech & Math, Kharkov, Ukraine
关键词
Incidence algebra; Poset;
D O I
10.1080/00927870802210019
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
It is well known that incidence algebras can be defined only for locally finite partially ordered sets (Doubilet et al., 1972; Stanley 1986). 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, 1986), 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 algebrafinitary 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.
引用
收藏
页码:1670 / 1676
页数:7
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