{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T20:57:42Z","timestamp":1757624262208,"version":"3.44.0"},"reference-count":8,"publisher":"SAGE Publications","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["COM"],"published-print":{"date-parts":[[2023,12,21]]},"abstract":"<jats:p>We consider a wide series of classes of algorithmic complexity. We fix such a class and investigate the complexity of the inversion operation in classical algebraic structures, like groups or fields. In addition, we analyze the properties of quotient structures.<\/jats:p>","DOI":"10.3233\/com-230459","type":"journal-article","created":{"date-parts":[[2023,12,22]],"date-time":"2023-12-22T10:56:18Z","timestamp":1703242578000},"page":"315-322","source":"Crossref","is-referenced-by-count":2,"title":["Inversion operations in algebraic structures"],"prefix":"10.1177","volume":"12","author":[{"given":"Pavel","family":"Alaev","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics, pr. Koptuga 4, Novosibirks, 630090, Russia"}]}],"member":"179","reference":[{"key":"10.3233\/COM-230459_ref1","unstructured":"A.V.\u00a0Aho, J.E.\u00a0Hopcroft and J.D.\u00a0Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974."},{"key":"10.3233\/COM-230459_ref2","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/978-3-031-09574-0_3","article-title":"Quotient structures and groups computable in polynomial time","volume":"13296","author":"Alaev","year":"2022","journal-title":"Lecture Notes in Computer Science"},{"issue":"6","key":"10.3233\/COM-230459_ref4","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/s10469-022-09661-3","article-title":"Fields of algebraic numbers computable in polynomial time. II","volume":"60","author":"Alaev","year":"2021","journal-title":"Algebra and Logic"},{"key":"10.3233\/COM-230459_ref5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-030-80049-9_1","article-title":"Searching for applicable versions of computable structures","volume":"12813","author":"Alaev","year":"2021","journal-title":"Lecture Notes in Computer Science"},{"issue":"1","key":"10.3233\/COM-230459_ref6","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/0168-0072(91)90008-A","article-title":"Polynomial time versus recursive models","volume":"54","author":"Cenzer","year":"1991","journal-title":"Annals of Pure and Applied Logic"},{"key":"10.3233\/COM-230459_ref7","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.tcs.2017.01.029","article-title":"Algebraic structures computable without delay","volume":"674","author":"Kalimullin","year":"2017","journal-title":"Theoretical Computer Science"},{"key":"10.3233\/COM-230459_ref8","unstructured":"S.\u00a0Lang, Algebra, Addison-Wesley Publishing Company, Reading, MA, 1965."},{"key":"10.3233\/COM-230459_ref9","doi-asserted-by":"crossref","unstructured":"B.L.\u00a0van der Waerden, Algebra I, Springer-Verlag, 1971.","DOI":"10.1007\/978-3-642-96044-4"}],"container-title":["Computability"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/COM-230459","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T12:22:17Z","timestamp":1757420537000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/COM-230459"}},"subtitle":[],"editor":[{"given":"Nikolay","family":"Bazhenov","sequence":"additional","affiliation":[]},{"given":"Takayuki","family":"Kihara","sequence":"additional","affiliation":[]},{"given":"Svetlana","family":"Selivanova","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2023,12,21]]},"references-count":8,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.3233\/com-230459","relation":{},"ISSN":["2211-3576","2211-3568"],"issn-type":[{"type":"electronic","value":"2211-3576"},{"type":"print","value":"2211-3568"}],"subject":[],"published":{"date-parts":[[2023,12,21]]}}}