{"title":"可分解性和可计算性","authors":"B. Khoussainov, A. G. Melnikov","doi":"10.1007/s10469-022-09683-x","DOIUrl":null,"url":null,"abstract":"<div><div><p>We present a new construction of indecomposable type <b>0</b> Abelian groups of rank 2. The new construction is used to study degree spectra of such groups. As a corollary, we obtain a new computability-theoretic proof showing that there exist continuum many nonisomorphic type <b>0</b> indecomposable Abelian groups of rank 2.</p></div></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Decomposability and Computability\",\"authors\":\"B. Khoussainov, A. G. Melnikov\",\"doi\":\"10.1007/s10469-022-09683-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div><p>We present a new construction of indecomposable type <b>0</b> Abelian groups of rank 2. The new construction is used to study degree spectra of such groups. As a corollary, we obtain a new computability-theoretic proof showing that there exist continuum many nonisomorphic type <b>0</b> indecomposable Abelian groups of rank 2.</p></div></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-10-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10469-022-09683-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10469-022-09683-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We present a new construction of indecomposable type 0 Abelian groups of rank 2. The new construction is used to study degree spectra of such groups. As a corollary, we obtain a new computability-theoretic proof showing that there exist continuum many nonisomorphic type 0 indecomposable Abelian groups of rank 2.
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