In a universal algebra, the concepts of minimum condition and maximum condition,descending chain condition and ascending chain condition for both -subalgebras and congruences are given in the paper; a set of necessary and sufficient conditions among the varied conditions are established subsequently.
本文在一个泛代数中给出了关于 －子代数及同余的极小条件、极大条件、降链条件和升链条件等概念，得到了反映这些概念间的关系的一组充要条件。