偏序集代数的同构问题

Isomorphism Problem of Partial Ordered Set Algebras

在[1]中对局部有限偏序集I={I,≤}及域K引入了关联代数KI的概念.这里的“局部有限”是指对任意a,b∈I,a≤b,集合{x∈I|a≤x≤b}.是有限集.KI的定义是:其元素是域K上以I中元素为行与列的足码的形式矩阵(кa,b)a,b∈I,(即允许有无限多个ka,b≠0)且满足条件:当a≮b时有ka,b=0.注意到I的局部有限性,易知上述形式矩阵的全体关于通常矩阵的加法和乘法以及数乘作成域K上的一个结合代数,称之为I在K上的关联代数KI。

Let I,I'be arbitrary partially ordered sets and F be a field. We introduce generalized path algebra, path algebra and partially ordered set algebra of / over F. In this paper we giVe the positive answer of isomorphism problem for these classes of algebras i.e. isomorphism of algebras of the same type, for example FI=FI', induces isomorphism of corresponding partial odered sets I and I'.