L-algebras and their ideals: from simplicity to semidirect products
Rings and Algebras
2025-12-10 v1 Combinatorics
Logic
Quantum Algebra
Abstract
In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidirect products and describe the structure of their prime spectrum. Furthermore, we introduce a family of finite simple L-algebras and prove that every simple linear L-algebra belongs to this family. We also show that the family we construct coincides with the class of simple algebras in a certain subclass of finite CKL-algebras. As an application, we use these results to give a clear description of linear Hilbert algebras and their symmetric semidirect products.
Cite
@article{arxiv.2512.08579,
title = {L-algebras and their ideals: from simplicity to semidirect products},
author = {Silvia Properzi and Yufei Qin},
journal= {arXiv preprint arXiv:2512.08579},
year = {2025}
}