---
_id: '58182'
abstract:
- lang: eng
  text: 'We study a weak divisibility property for noncommutative rings: a nontrivial
    ring is fadelian if for all nonzero a and x there exist b, c such that x=ab+ca.
    We prove properties of fadelian rings and construct examples thereof which are
    not division rings, as well as non-Noetherian and non-Ore examples.'
author:
- first_name: Robin
  full_name: Khanfir, Robin
  last_name: Khanfir
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Khanfir R, Seguin BF. Study of a division-like property. <i>Journal of Algebra
    and Its Applications</i>. Published online 2024. doi:<a href="https://doi.org/10.1142/s0219498825502214">10.1142/s0219498825502214</a>
  apa: Khanfir, R., &#38; Seguin, B. F. (2024). Study of a division-like property.
    <i>Journal of Algebra and Its Applications</i>. <a href="https://doi.org/10.1142/s0219498825502214">https://doi.org/10.1142/s0219498825502214</a>
  bibtex: '@article{Khanfir_Seguin_2024, title={Study of a division-like property},
    DOI={<a href="https://doi.org/10.1142/s0219498825502214">10.1142/s0219498825502214</a>},
    journal={Journal of Algebra and Its Applications}, publisher={World Scientific
    Pub Co Pte Ltd}, author={Khanfir, Robin and Seguin, Beranger Fabrice}, year={2024}
    }'
  chicago: Khanfir, Robin, and Beranger Fabrice Seguin. “Study of a Division-like
    Property.” <i>Journal of Algebra and Its Applications</i>, 2024. <a href="https://doi.org/10.1142/s0219498825502214">https://doi.org/10.1142/s0219498825502214</a>.
  ieee: 'R. Khanfir and B. F. Seguin, “Study of a division-like property,” <i>Journal
    of Algebra and Its Applications</i>, 2024, doi: <a href="https://doi.org/10.1142/s0219498825502214">10.1142/s0219498825502214</a>.'
  mla: Khanfir, Robin, and Beranger Fabrice Seguin. “Study of a Division-like Property.”
    <i>Journal of Algebra and Its Applications</i>, World Scientific Pub Co Pte Ltd,
    2024, doi:<a href="https://doi.org/10.1142/s0219498825502214">10.1142/s0219498825502214</a>.
  short: R. Khanfir, B.F. Seguin, Journal of Algebra and Its Applications (2024).
date_created: 2025-01-15T10:59:30Z
date_updated: 2025-01-15T11:35:29Z
doi: 10.1142/s0219498825502214
language:
- iso: eng
main_file_link:
- url: https://beranger-seguin.fr/dmi/fadelian/fadrings.pdf
publication: Journal of Algebra and Its Applications
publication_identifier:
  issn:
  - 0219-4988
  - 1793-6829
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Study of a division-like property
type: journal_article
user_id: '102487'
year: '2024'
...
---
_id: '33262'
abstract:
- lang: eng
  text: The authors of Berg et al. [J. Algebra 348 (2011) 446–461] provide an algorithm
    for finding a complete system of primitive orthogonal idempotents for CM, where
    M is any finite R-trivial monoid. Their method relies on a technical result stating
    that R-trivial monoid are equivalent to so-called weakly ordered monoids. We provide
    an alternative algorithm, based only on the simple observation that an R-trivial
    monoid may be realized by upper triangular matrices. This approach is inspired
    by results in the field of coupled cell network dynamical systems, where L-trivial
    monoids (the opposite notion) correspond to so-called feed-forward networks. We
    first show that our algorithm works for ZM, after which we prove that it also
    works for RM where R is an arbitrary ring with a known complete system of primitive
    orthogonal idempotents. In particular, our algorithm works if R is any field.
    In this respect our result constitutes a considerable generalization of the results
    in Berg et al. [J. Algebra 348 (2011) 446–461]. Moreover, the system of idempotents
    for RM is obtained from the one our algorithm yields for ZM in a straightforward
    manner. In other words, for any finite R-trivial monoid M our algorithm only has
    to be performed for ZM, after which a system of idempotents follows for any ring
    with a given system of idempotents.
author:
- first_name: Eddie
  full_name: Nijholt, Eddie
  last_name: Nijholt
- first_name: Bob
  full_name: Rink, Bob
  last_name: Rink
- first_name: Sören
  full_name: Schwenker, Sören
  id: '97359'
  last_name: Schwenker
  orcid: 0000-0002-8054-2058
citation:
  ama: Nijholt E, Rink B, Schwenker S. A new algorithm for computing idempotents of
    ℛ-trivial monoids. <i>Journal of Algebra and Its Applications</i>. 2020;20(12).
    doi:<a href="https://doi.org/10.1142/s0219498821502273">10.1142/s0219498821502273</a>
  apa: Nijholt, E., Rink, B., &#38; Schwenker, S. (2020). A new algorithm for computing
    idempotents of ℛ-trivial monoids. <i>Journal of Algebra and Its Applications</i>,
    <i>20</i>(12). <a href="https://doi.org/10.1142/s0219498821502273">https://doi.org/10.1142/s0219498821502273</a>
  bibtex: '@article{Nijholt_Rink_Schwenker_2020, title={A new algorithm for computing
    idempotents of ℛ-trivial monoids}, volume={20}, DOI={<a href="https://doi.org/10.1142/s0219498821502273">10.1142/s0219498821502273</a>},
    number={12}, journal={Journal of Algebra and Its Applications}, publisher={World
    Scientific Pub Co Pte Ltd}, author={Nijholt, Eddie and Rink, Bob and Schwenker,
    Sören}, year={2020} }'
  chicago: Nijholt, Eddie, Bob Rink, and Sören Schwenker. “A New Algorithm for Computing
    Idempotents of ℛ-Trivial Monoids.” <i>Journal of Algebra and Its Applications</i>
    20, no. 12 (2020). <a href="https://doi.org/10.1142/s0219498821502273">https://doi.org/10.1142/s0219498821502273</a>.
  ieee: 'E. Nijholt, B. Rink, and S. Schwenker, “A new algorithm for computing idempotents
    of ℛ-trivial monoids,” <i>Journal of Algebra and Its Applications</i>, vol. 20,
    no. 12, 2020, doi: <a href="https://doi.org/10.1142/s0219498821502273">10.1142/s0219498821502273</a>.'
  mla: Nijholt, Eddie, et al. “A New Algorithm for Computing Idempotents of ℛ-Trivial
    Monoids.” <i>Journal of Algebra and Its Applications</i>, vol. 20, no. 12, World
    Scientific Pub Co Pte Ltd, 2020, doi:<a href="https://doi.org/10.1142/s0219498821502273">10.1142/s0219498821502273</a>.
  short: E. Nijholt, B. Rink, S. Schwenker, Journal of Algebra and Its Applications
    20 (2020).
date_created: 2022-09-06T11:37:00Z
date_updated: 2022-09-07T08:35:24Z
doi: 10.1142/s0219498821502273
extern: '1'
external_id:
  arxiv:
  - '1906.02844'
intvolume: '        20'
issue: '12'
keyword:
- Applied Mathematics
- Algebra and Number Theory
language:
- iso: eng
publication: Journal of Algebra and Its Applications
publication_identifier:
  issn:
  - 0219-4988
  - 1793-6829
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: A new algorithm for computing idempotents of ℛ-trivial monoids
type: journal_article
user_id: '97359'
volume: 20
year: '2020'
...