[{"title":"Study of a division-like property","main_file_link":[{"url":"https://beranger-seguin.fr/dmi/fadelian/fadrings.pdf"}],"doi":"10.1142/s0219498825502214","publisher":"World Scientific Pub Co Pte Ltd","date_updated":"2025-01-15T11:35:29Z","date_created":"2025-01-15T10:59:30Z","author":[{"last_name":"Khanfir","full_name":"Khanfir, Robin","first_name":"Robin"},{"last_name":"Seguin","id":"102487","full_name":"Seguin, Beranger Fabrice","first_name":"Beranger Fabrice"}],"year":"2024","citation":{"short":"R. Khanfir, B.F. Seguin, Journal of Algebra and Its Applications (2024).","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} }","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>.","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>","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>","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>.","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>."},"publication_status":"published","publication_identifier":{"issn":["0219-4988","1793-6829"]},"language":[{"iso":"eng"}],"_id":"58182","user_id":"102487","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."}],"status":"public","type":"journal_article","publication":"Journal of Algebra and Its Applications"},{"year":"2020","issue":"12","title":"A new algorithm for computing idempotents of ℛ-trivial monoids","publisher":"World Scientific Pub Co Pte Ltd","date_created":"2022-09-06T11:37:00Z","abstract":[{"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.","lang":"eng"}],"publication":"Journal of Algebra and Its Applications","keyword":["Applied Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["1906.02844"]},"intvolume":"        20","citation":{"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>","short":"E. Nijholt, B. Rink, S. Schwenker, Journal of Algebra and Its Applications 20 (2020).","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} }","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>.","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>","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>."},"publication_identifier":{"issn":["0219-4988","1793-6829"]},"publication_status":"published","doi":"10.1142/s0219498821502273","date_updated":"2022-09-07T08:35:24Z","volume":20,"author":[{"last_name":"Nijholt","full_name":"Nijholt, Eddie","first_name":"Eddie"},{"first_name":"Bob","full_name":"Rink, Bob","last_name":"Rink"},{"orcid":"0000-0002-8054-2058","last_name":"Schwenker","id":"97359","full_name":"Schwenker, Sören","first_name":"Sören"}],"status":"public","type":"journal_article","extern":"1","_id":"33262","user_id":"97359"}]