交换半环上极大同余的一些性质

Some Properties of Maximal Congruences on Commutative Semirings

研究由理想生成的同余与生成理想的对应关系,由商半环和同余的元素给出极大同余的充要条件;同时定义拟极大同余,借助拟极大同余讨论极大同余的生成理想;最后讨论降链条件下的极大同余的性质.

In this paper,we discuss the relationship between congruences and theirs generated ideals.The sufficient and necessary conditions for a congruence to be a maximal congruence are described by the semirings of quotient by this congruence and elements of the congruence.At the same time,we define a concept of quasi-maximal congruence,to discuss the generating ideals of maximal con-gruences by means of quasi-maximal congruences.Finally,we discuss the properties of maximal congruences in semirings satisfying the descending chain condition.