@article{Zhao2024, 
author = {Ziteng Zhao and Jing Wang and Yali Wu},
title = {Note on  p-ideals set of orthomodular lattices},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {31947-31961},
keywords = {orthomodular lattices, OM-L-algebras, p-ideals, L-ideals, well ordered},
url = {https://www.sciopen.com/article/10.3934/math.20241535},
doi = {10.3934/math.20241535},
abstract = {This paper mainly discusses the problems raised in Kalmbach's book: When are the  p-ideals of an irreducible orthomodular lattice well ordered under set inclusion? We give three classes of orthomodular lattices whose  p-ideals set is a chain under set inclusion. Furthermore, this article also provides a sufficient and necessary condition for the  p-ideals set of orthomodular lattices to be a chain under set inclusion from the perspective of  L-algebras, which gives a new point to solve the questions. Moveover, we also give some characterizations about central elements of orthomodular lattice.}
}