{"title":"论可解鲍姆斯拉格-索利塔群的完形基本理论","authors":"N. S. Romanovskiy","doi":"10.1134/S1064562424601239","DOIUrl":null,"url":null,"abstract":"<p>We define a divisible completion of the solvable Baumslag-Solitar group <span>\\(BS(1,n)\\)</span> and prove that under certain restrictions on <i>n</i> the elementary theory of this completion is decidable.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"109 3","pages":"268 - 270"},"PeriodicalIF":0.5000,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Elementary Theory of Completion of Solvable Baumslag–Solitar Group\",\"authors\":\"N. S. Romanovskiy\",\"doi\":\"10.1134/S1064562424601239\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We define a divisible completion of the solvable Baumslag-Solitar group <span>\\\\(BS(1,n)\\\\)</span> and prove that under certain restrictions on <i>n</i> the elementary theory of this completion is decidable.</p>\",\"PeriodicalId\":531,\"journal\":{\"name\":\"Doklady Mathematics\",\"volume\":\"109 3\",\"pages\":\"268 - 270\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1064562424601239\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424601239","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们定义了可解 Baumslag-Solitar 群 \(BS(1,n)\)的可分完成，并证明在 n 的某些限制条件下，这个完成的基本理论是可解的。
On Elementary Theory of Completion of Solvable Baumslag–Solitar Group
We define a divisible completion of the solvable Baumslag-Solitar group \(BS(1,n)\) and prove that under certain restrictions on n the elementary theory of this completion is decidable.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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