Abstract: A（M）-completely regular semiring is introduces， and the closed relationship between the subdirect product decomposition of A（M）-completely regular semiring and the subdirect product decomposition of its additive （multiplicative） reduct is given by using the concept of sturdy frame of type （2，2） algebras.In particular，some results in references are extended.

Key words: variety, Mal’cev product, subdirect product, sturdy frame

摘要： 介绍了A（M）-完全正则半环，并利用（2，2）型代数的坚固构架的概念，给出了A（M）-完全正则半环的次直积分解与其加法（乘法）半群的次直积分解之间的密切联系。特别地，推广了以往文献的一些结果。

关键词: 簇, Mal’cev积, 次直积, 坚固构架