{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:25Z","timestamp":1760240005640,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,13]],"date-time":"2019-02-13T00:00:00Z","timestamp":1550016000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we develop the theory of SAGBI bases in G-algebras and create a criterion through which we can check if a set of polynomials in a G-algebra is a SAGBI basis or not. Moreover, we will construct an algorithm to compute SAGBI bases from a subset of polynomials contained in a subalgebra of a G-algebra.<\/jats:p>","DOI":"10.3390\/sym11020221","type":"journal-article","created":{"date-parts":[[2019,2,14]],"date-time":"2019-02-14T03:21:46Z","timestamp":1550114506000},"page":"221","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["SAGBI Bases in G-Algebras"],"prefix":"10.3390","volume":"11","author":[{"given":"Muhammad Abdul Basit","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Institute of Business Administration, Karachi-75270, Pakistan"}]},{"given":"Junaid","family":"Alam Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Institute of Business Administration, Karachi-75270, Pakistan"}]},{"given":"Muhammad Ahsan","family":"Binyamin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, GC University, Faisalabad-38000, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,13]]},"reference":[{"key":"ref_1","unstructured":"Levandovskyy, V. 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Effective Algorithms for Intrinsically Computing SA GBI-Groebner Bases in a Polynomial Ring over a Field, Cambridge University Press.","DOI":"10.1017\/CBO9780511565847.025"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/221\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:31:52Z","timestamp":1760185912000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/221"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,13]]},"references-count":18,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["sym11020221"],"URL":"https:\/\/doi.org\/10.3390\/sym11020221","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,2,13]]}}}