{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T06:18:07Z","timestamp":1774592287991,"version":"3.50.1"},"reference-count":37,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","funder":[{"name":"Russian Foundation for Basic Research","award":["17-01-00247"],"award-info":[{"award-number":["17-01-00247"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2020,2]]},"abstract":"<jats:p> We use computability-theoretic tools to measure the complexity of the process of direct decomposing an abelian group based on its symbolic presentation. More specifically, we compare degrees of decidable categoricity of abelian groups with degrees of categoricity of their natural direct summands. As a nontrivial and unexpected application of our methods, we show that every decidable copy of a nondivisible homogeneous completely decomposable group has an algorithm for linear independence. <\/jats:p>","DOI":"10.1142\/s0218196719500644","type":"journal-article","created":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T07:56:20Z","timestamp":1566806180000},"page":"49-90","source":"Crossref","is-referenced-by-count":2,"title":["Decompositions of decidable abelian groups"],"prefix":"10.1142","volume":"30","author":[{"given":"Nikolay","family":"Bazhenov","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics, Akad. Koptyug Ave. 4, Novosibirsk 630090, Russia"},{"name":"Novosibirsk State University, 2 Pirogova St., Novosibirsk 630090, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergey","family":"Goncharov","sequence":"additional","affiliation":[{"name":"Sobolev Institute of Mathematics, Akad. Koptyug Ave. 4, Novosibirsk 630090, Russia"},{"name":"Novosibirsk State University, 2 Pirogova St., Novosibirsk 630090, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Melnikov","sequence":"additional","affiliation":[{"name":"Massey University Auckland, Private Bag 102904, North Shore, Auckland 0745, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,10,15]]},"reference":[{"key":"S0218196719500644BIB001","series-title":"Studies in Logic and the Foundations of Mathematics","volume-title":"Computable Structures and the Hyperarithmetical Hierarchy","volume":"144","author":"Ash C.","year":"2000"},{"key":"S0218196719500644BIB003","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-37-00308-9"},{"key":"S0218196719500644BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00045-5"},{"key":"S0218196719500644BIB005","doi-asserted-by":"publisher","DOI":"10.1017\/S096012951600030X"},{"key":"S0218196719500644BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s10469-016-9395-4"},{"key":"S0218196719500644BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.11.003"},{"key":"S0218196719500644BIB008","volume-title":"Model Theory","author":"Chang C. C.","year":"1973"},{"key":"S0218196719500644BIB009","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-1960479"},{"issue":"2","key":"S0218196719500644BIB010","first-page":"18","volume":"24","author":"Dobritsa V. P.","year":"1983","journal-title":"Sibirsk. Mat. Zh."},{"key":"S0218196719500644BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2012.09.020"},{"key":"S0218196719500644BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196714500465"},{"key":"S0218196719500644BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2016.04.016"},{"key":"S0218196719500644BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.06.007"},{"key":"S0218196719500644BIB015","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2014-06115-1"},{"key":"S0218196719500644BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-4305-3"},{"key":"S0218196719500644BIB017","volume-title":"Decidability Problems and Constructive Models","author":"Ershov Yu. L.","year":"1980"},{"key":"S0218196719500644BIB018","series-title":"Siberian School of Algebra and Logic","volume-title":"Definability and Computability","author":"Ershov Y. L.","year":"1996"},{"key":"S0218196719500644BIB019","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107338579.006"},{"key":"S0218196719500644BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-009-0160-4"},{"key":"S0218196719500644BIB021","volume-title":"Infinite Abelian Groups. Vol. II","author":"Fuchs L.","year":"1973"},{"issue":"1","key":"S0218196719500644BIB022","first-page":"23","volume":"19","author":"Goncharov S.","year":"1980","journal-title":"Algebra i Logika"},{"key":"S0218196719500644BIB023","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021758312697"},{"key":"S0218196719500644BIB024","doi-asserted-by":"publisher","DOI":"10.1134\/S0081543811060071"},{"key":"S0218196719500644BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2015.06.004"},{"issue":"2","key":"S0218196719500644BIB026","first-page":"68","volume":"2","author":"Khisamiev N. G.","year":"1992","journal-title":"Siberian Adv. Math."},{"key":"S0218196719500644BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80050-5"},{"key":"S0218196719500644BIB031","first-page":"1431","volume":"3","author":"Mal\u2019tsev A. I.","year":"1962","journal-title":"Sov. Math. Dokl."},{"key":"S0218196719500644BIB032","first-page":"987","volume":"3","author":"Mal\u2019tsev A. I.","year":"1962","journal-title":"Sov. Math. Dokl."},{"key":"S0218196719500644BIB033","doi-asserted-by":"publisher","DOI":"10.1017\/bsl.2014.32"},{"key":"S0218196719500644BIB034","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2017.12.011"},{"key":"S0218196719500644BIB035","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2012.11.012"},{"key":"S0218196719500644BIB036","doi-asserted-by":"publisher","DOI":"10.1007\/BF01463352"},{"key":"S0218196719500644BIB037","first-page":"341","volume":"95","author":"Rabin M.","year":"1960","journal-title":"Trans. Amer. Math. Soc."},{"key":"S0218196719500644BIB038","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/12509"},{"key":"S0218196719500644BIB039","first-page":"333","volume":"227","author":"Rogers L. A.","year":"1977","journal-title":"Trans. Amer. Math. Soc."},{"key":"S0218196719500644BIB040","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0090954"},{"key":"S0218196719500644BIB041","doi-asserted-by":"publisher","DOI":"10.4064\/fm-41-2-203-271"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196719500644","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T02:46:54Z","timestamp":1581302814000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196719500644"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,15]]},"references-count":37,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2020,2]]}},"alternative-id":["10.1142\/S0218196719500644"],"URL":"https:\/\/doi.org\/10.1142\/s0218196719500644","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,15]]}}}