关于L-代数中理想的一些注记  

Notes on L- Ideals of L- Algebras

作　　者：尹丽云 钟晨 吴雅丽 YIN Liyun;ZHONG Chen;WU Yali(School of Mathematics and Science,Hebei GEO University,Shijiazhuang 050031,Hebei)

机构地区：[1]河北地质大学数理教学部,河北石家庄050031

出　　处：《四川师范大学学报（自然科学版）》2025年第2期270-278,共9页Journal of Sichuan Normal University（Natural Science）

基　　金：河北省自然科学青年基金(A2019403031)。

摘　　要：许多逻辑代数可以看成L-代数.讨论一些特殊的L-代数,给出其L-理想与格滤子之间的关系.刻画一类使得L-理想集与格滤子集相等的格L-代数,同时给出L-代数与蕴含格之间的一个等价刻画.进一步给出格序效应代数的理想与L-理想以及它的同余与L-同余的等价刻画.It is well known that many logical algebras can be regarded as L- algebras. In this paper, we discusses some specialL- algebras and give the relation between L- ideals and lattice filters. Moreover, we characterize a class of lattice Lalgebrasthat make the L- ideal sets equal to lattice filter sets, and where an equivalent characterization between Lalgebrasand implicative lattices is also given. Furthermore, we give the equivalent characterizations of ideals and Lidealsof lattice-ordered effect algebras and as well as its congruences and L- congruences.

关 键 词：L-代数 格序效应代数 L-理想 蕴含格 滤子 

分 类 号：O159[理学—数学]