{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:20:51Z","timestamp":1760149251047,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T00:00:00Z","timestamp":1690329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSPD2023R545"],"award-info":[{"award-number":["RSPD2023R545"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Suppose R is a finite chain ring with invaraints p,n,r,k,k\u2032,m. Suppose G is also the subset of all \u03c6\u2208 Aut(R), the automorphism group of R, such that \u03c6(\u03c0k\u2032)=\u03c0k\u2032, where \u03c0 is a generator of the maximal ideal of R. It was found that G is a group that is, in some sense, the set of all symmetries of {\u03c0k\u2032}. The main purpose of this article is to describe the structure of G. The subgroup G helps us understand the structure of Aut(R) in the general case which in turn provides immediate results in classifying chain rings.<\/jats:p>","DOI":"10.3390\/sym15081482","type":"journal-article","created":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T01:27:46Z","timestamp":1690421266000},"page":"1482","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Automorphisms of Chain Rings"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6824-6985","authenticated-orcid":false,"given":"Sami","family":"Alabiad","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5779-0520","authenticated-orcid":false,"given":"Yousef","family":"Alkhamees","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-2520-2699","authenticated-orcid":false,"given":"Alhanouf Ali","family":"Alhomaidhi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Serre, J., and Greenberg, M. 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