{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:46:37Z","timestamp":1760143597695,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,17]],"date-time":"2024-02-17T00:00:00Z","timestamp":1708128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005033","name":"Bialystok University of Technology","doi-asserted-by":"publisher","award":["WZ\/WI-IIT\/2\/2022"],"award-info":[{"award-number":["WZ\/WI-IIT\/2\/2022"]}],"id":[{"id":"10.13039\/501100005033","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Sylvester-polynomial-conjugate matrix equations unify many well-known versions and generalizations of the Sylvester matrix equation AX\u2212XB=C which have a wide range of applications. In this paper, we present a general approach to Sylvester-polynomial-conjugate matrix equations via groupoids, vector spaces, and matrices over skew polynomial rings. The obtained results are applied to Sylvester-polynomial-conjugate matrix equations over complex numbers and quaternions. The main role in our approach is played by skew polynomial rings, which are well-known tools in algebra to provide examples of asymmetry between left-sided and right-sided versions of many ring objects.<\/jats:p>","DOI":"10.3390\/sym16020246","type":"journal-article","created":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T10:40:15Z","timestamp":1708339215000},"page":"246","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A General Approach to Sylvester-Polynomial-Conjugate Matrix Equations"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1093-7177","authenticated-orcid":false,"given":"Ryszard","family":"Mazurek","sequence":"first","affiliation":[{"name":"Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bia\u0142ystok, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,17]]},"reference":[{"key":"ref_1","unstructured":"Strang, G. 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