Chains of Semiprime and Prime Ideals in Leavitt Path Algebras
Rings and Algebras
2019-04-01 v1
Abstract
Semiprime ideals of an arbitrary Leavitt path algebra L are described in terms of their generators. This description is then used to show that the semiprime ideals form a complete sublattice of the lattice of ideals of L, and they enjoy a certain gap property identified by Kaplansky in prime spectra of commutative rings. It is also shown that the totally ordered sets that can be realized as prime spectra of Leavitt path algebras are precisely those that have greatest lower bounds on subchains and enjoy the aforementioned gap property. Finally, it is shown that a conjecture of Kaplansky regarding identifying von Neumann regular rings via their prime factors holds for Leavitt path algebras.
Keywords
Cite
@article{arxiv.1712.01803,
title = {Chains of Semiprime and Prime Ideals in Leavitt Path Algebras},
author = {Gene Abrams and Be'eri Greenfeld and Zachary Mesyan and Kulumani M. Rangaswamy},
journal= {arXiv preprint arXiv:1712.01803},
year = {2019}
}
Comments
15 pages