{"author":[{"first_name":"Eddie","last_name":"Nijholt","full_name":"Nijholt, Eddie"},{"first_name":"Bob","last_name":"Rink","full_name":"Rink, Bob"},{"id":"97359","first_name":"Sören","last_name":"Schwenker","orcid":"0000-0002-8054-2058","full_name":"Schwenker, Sören"}],"status":"public","user_id":"97359","title":"A new algorithm for computing idempotents of ℛ-trivial monoids","publisher":"World Scientific Pub Co Pte Ltd","publication_status":"published","external_id":{"arxiv":["1906.02844"]},"volume":20,"intvolume":"        20","type":"journal_article","date_updated":"2022-09-07T08:35:24Z","citation":{"short":"E. Nijholt, B. Rink, S. Schwenker, Journal of Algebra and Its Applications 20 (2020).","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>.","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>.","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>.","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>","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>","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} }"},"publication_identifier":{"issn":["0219-4988","1793-6829"]},"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."}],"language":[{"iso":"eng"}],"_id":"33262","year":"2020","publication":"Journal of Algebra and Its Applications","date_created":"2022-09-06T11:37:00Z","extern":"1","doi":"10.1142/s0219498821502273","keyword":["Applied Mathematics","Algebra and Number Theory"],"issue":"12"}