关于G-代数的一些注记

Some Notes on G-algebras

引进了基于一般剩余格的G-代数—G(RL)-代数的概念,并且分别给出了G-滤子和(全序)G(RL)-代数的一系列特征刻画,同时还证明了任何正则的G(RL)-代数必为Boolean代数。本文所得结果分别是已有结果的一般化。

In this paper, the concept of G（RL）-algebras based on general residuated lattices is introduced, and some characterizations of G-filters and （totally ordered） G（RL）-algebras are respectively established. Moreover, it is proved that any regular G （RL）-algebra is a Boolean algebra. These results are respectively a generalization of some early results presented in the references.