{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:40:24Z","timestamp":1760060424838,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,30]],"date-time":"2025-08-30T00:00:00Z","timestamp":1756512000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Xiamen University of Technology High level Talents Research Launch Project","award":["YKJ24039R","JAT241124"],"award-info":[{"award-number":["YKJ24039R","JAT241124"]}]},{"name":"Fujian Province Young and Middle-aged Teacher Education Research Project","award":["YKJ24039R","JAT241124"],"award-info":[{"award-number":["YKJ24039R","JAT241124"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A polynomial is called a generalized multilinear polynomial if it is a sum of some multilinear polynomials over a field. The goal of this paper is to give a description of the images of generalized multilinear polynomials on upper triangular matrix algebras, generalizing all results of the Fagundes\u2013Mello conjecture proposed by Fagundes and Mello in 2019.<\/jats:p>","DOI":"10.3390\/axioms14090671","type":"journal-article","created":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T13:01:13Z","timestamp":1756818073000},"page":"671","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Images of Generalized Multilinear Polynomials on Upper Triangular Matrix Algebras"],"prefix":"10.3390","volume":"14","author":[{"given":"Qian","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Xiamen University of Technology, Xiamen 361024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,30]]},"reference":[{"key":"ref_1","first-page":"071","article-title":"Evaluations of noncommutative polynomials on algebras: Methods and problems, and the Lvov-Kaplansky conjecture","volume":"16","author":"Malev","year":"2020","journal-title":"SIGMA"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.laa.2018.11.014","article-title":"The images of multilinear polynomials on strictly upper triangular matrices","volume":"563","author":"Fagundes","year":"2019","journal-title":"Linear Algebra Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"283","DOI":"10.7153\/oam-2019-13-18","article-title":"Images of multilinear polynomials of degree up to four on upper triangular matrices","volume":"13","author":"Fagundes","year":"2019","journal-title":"Oper. 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