{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T11:57:03Z","timestamp":1762516623610,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T00:00:00Z","timestamp":1762473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Scientific Research Projects of Henan Higher Education Institutions","award":["25A160001","26B110007"],"award-info":[{"award-number":["25A160001","26B110007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We investigate the relationships between the weak resolution dimensions of subcategories of module categories of Artinian algebras in the present paper. Let \u039b be an Artinian algebra, and A, B and X subcategories of \u039b-modules, such that each object X in X is given by an exact sequence 0\u2192A\u2192B\u2192X\u21920 with A\u2208ObA and B\u2208ObB. We prove that the weak resolution dimension of X is bounded above by the sum of the corresponding dimensions for A and B plus 1. As applications, we study weak resolution dimensions of Artinian algebras under left idealized extensions and conditions on special ideals.<\/jats:p>","DOI":"10.3390\/axioms14110824","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T11:41:47Z","timestamp":1762515707000},"page":"824","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Weak Resolution Dimensions of Subcategories"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-0214-100X","authenticated-orcid":false,"given":"Juxiang","family":"Sun","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinpeng","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Accounting and Finance, Hong Kong Polytechnic University, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weimin","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Physics, Shangqiu Normal University, Shangqiu 476000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,7]]},"reference":[{"key":"ref_1","first-page":"505","article-title":"Representation Dimension of Artinian Algebras","volume":"Volume 1","author":"Auslander","year":"1999","journal-title":"Selected Works of Maurice Auslander"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1090\/S0002-9939-02-06616-9","article-title":"Finiteness of representation dimension","volume":"131","author":"Iyama","year":"2003","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1215\/00127094-2009-025","article-title":"Lower bounds for Auslander\u2019s representation dimension","volume":"148","author":"Oppermann","year":"2009","journal-title":"Duke Math. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.jalgebra.2022.08.024","article-title":"The derived dimensions of (m, n)-Igusa-Todorov algebras","volume":"612","author":"Zheng","year":"2022","journal-title":"J. Algebra"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s00013-024-02030-9","article-title":"The derived dimensions and representation distances of Artinian algebras","volume":"123","author":"Zheng","year":"2024","journal-title":"Arch. Math."},{"key":"ref_6","unstructured":"Zhang, J., and Zheng, J. (2024). Igusa-Todorov distances. arXiv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2215","DOI":"10.1016\/j.aim.2009.07.008","article-title":"Finitistic dimension and Igusa\u2013Todorov algebras","volume":"222","author":"Wei","year":"2009","journal-title":"Adv. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1515\/form.2011.019","article-title":"Finitistic dimension conjecture and conditions on ideals","volume":"23","author":"Wei","year":"2011","journal-title":"Forum Math."},{"key":"ref_9","unstructured":"Iyama, O. (2003). Rejective subcategories of Artinian algebras and orders. arXiv."},{"key":"ref_10","first-page":"116","article-title":"On the finitistic dimension conjecture II: Related to finite global dimension","volume":"201","author":"Xi","year":"2006","journal-title":"J. Pure Appl. Algebra"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.jpaa.2004.03.009","article-title":"On the finitistic dimension conjecture I: Related to representation-finite algebras","volume":"193","author":"Xi","year":"2004","journal-title":"J. Pure Appl. Algebra"},{"key":"ref_12","first-page":"340","article-title":"On the finitistic dimension conjecture","volume":"2","author":"Xi","year":"2005","journal-title":"Oberwolfach Rep."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/11\/824\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T11:53:10Z","timestamp":1762516390000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/11\/824"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,7]]},"references-count":12,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["axioms14110824"],"URL":"https:\/\/doi.org\/10.3390\/axioms14110824","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,11,7]]}}}