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PreprintCC BY 4.0arXiv

On The Cyclicity of Algebraic Lattices

  • Maria Fernanda Zordan Bonini
  • Robson Ricardo de Araujo
  • Antonio Aparecido de Andrade
  • Jéfferson Luiz Rocha Bastos
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Abstract

This work presents theoretical advances in the study of cyclic and quasi-cyclic lattices. First, we provide elementary facts regarding cyclic and quasi-cyclic lattices, and discuss about the cyclicity of some notable lattices. The main contributions of the paper is in the algebraic setting: we investigate cyclic lattices arising from ℤ-modules in Galois number fields via the Minkowski embedding. We establish necessary and sufficient conditions for an algebraic lattice to be cyclic over both cyclic and general Galois number fields, expressed in terms of naturally associated groups. Moreover, we derive a necessary and sufficient condition for ideal lattices to be cyclic, depending on the factorization of the ideal in the underlying number field.

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Cite

BibTeXRIS
BibTeX
@misc{bonini2026cyclicity,
  title = {{On The Cyclicity of Algebraic Lattices}},
  author = {Maria Fernanda Zordan Bonini and Robson Ricardo de Araujo and Antonio Aparecido de Andrade and Jéfferson Luiz Rocha Bastos},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21174},
  eprint = {2609.21174},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21174},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On The Cyclicity of Algebraic Lattices
AU  - Maria Fernanda Zordan Bonini
AU  - Robson Ricardo de Araujo
AU  - Antonio Aparecido de Andrade
AU  - Jéfferson Luiz Rocha Bastos
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21174
UR  - https://arxiv.org/abs/2609.21174
AB  - This work presents theoretical advances in the study of cyclic and quasi-cyclic lattices. First, we provide elementary facts regarding cyclic and quasi-cyclic lattices, and discuss about the cyclicity of some notable lattices. The main contributions of the paper is in the algebraic setting: we investigate cyclic lattices arising from ℤ-modules in Galois number fields via the Minkowski embedding. We establish necessary and sufficient conditions for an algebraic lattice to be cyclic over both cyclic and general Galois number fields, expressed in terms of naturally associated groups. Moreover, we derive a necessary and sufficient condition for ideal lattices to be cyclic, depending on the factorization of the ideal in the underlying number field.
ER  -