2025/06/09 by He, Peng, Wang, Xue-ping
#03B52 #03E72 #03G10 #06B05 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2506.07567
This article focuses on the relationship between pseudo-t-norms and the structure of lattices. First, we establish a necessary and sufficient condition for the existence of a left-continuous t-norm on the ordinal sum of two disjoint complete lattices. Then, we define the 1-distributivity of a lattice, which is applied for characterizing a complete atomistic lattice that has a left-continuous pseudo-t-norm. We also describe the forbidden structures of a finite modular lattice that is a 1-distributive lattice, which is used for representing a kind of finite planar modular lattices that have left-continuous pseudo-t-norms.