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On the existence of divisible non-injective modules over Leavitt path algebras
Abstract
Let K be any field and E any directed graph. We investigate the existence of divisible non-injective left modules over the Leavitt path algebra L_K(E) for a broad class of graphs. Our main tool is a general criterion for divisibility that is particularly well suited to our setting.
Related
- The injective envelope of simple modules over Leavitt path algebras I: simple left ideals
- The injective envelope of simple modules over Leavitt path algebras II: simples arising from exclusive cycles
- Simple Modules over Leavitt Path Algebras Generated by Indicator Functions on Paths
- STRONGLY ϕ-FLAT MODULES, STRONGLY NONNIL-INJECTIVE MODULES AND THEIR HOMOLOGICAL DIMENSIONS
- Structure of irreducible homomorphisms to/from free and injective modules
BibTeX
@misc{barban2026existence,
title = {{On the existence of divisible non-injective modules over Leavitt path algebras}},
author = {Mara Barban and Alberto Tonolo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24486},
eprint = {2609.24486},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24486},
}
RIS
TY - UNPB
TI - On the existence of divisible non-injective modules over Leavitt path algebras
AU - Mara Barban
AU - Alberto Tonolo
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24486
UR - https://arxiv.org/abs/2609.24486
AB - Let K be any field and E any directed graph. We investigate the existence of divisible non-injective left modules over the Leavitt path algebra L_K(E) for a broad class of graphs. Our main tool is a general criterion for divisibility that is particularly well suited to our setting.
ER -