代数上的一类同余的注记

同余是泛代数的重要研究内容,泛代数上的同余在一定意义上能够刻画和确定泛代数的结构和性质。首先引入了一个泛代数上的渗透一个子集合的最大同余的概念,然后对其性质进行了刻画。最后利用该同余给出了关于平凡代数的几个等价条件,证明了泛代数的子集到渗透该集的最大同余的映射为保序映射。该映射为∩-同态、该泛代数平凡等是等价的。

A Note on Certain Congruences on an Algebra

The concept of congruence is an important content of the universal algebra and congruences play a fundamental role in defining the structure and properties of the universal algebra. In this paper the notion of the greatest saturating congruence on an algebra is introduced and properties of these congruences are characterized. Further some equivalent conditions for a trivial algebra are given, and that the mapping which maps the subset of the universal to the maximal congruence that saturates the subset being a -homomorphism, being order preserving, being constant mapping, the algebra being trivial are equivalent is proved.