{"title":"ITBM-算法的构造补全","authors":"A. S. Morozov","doi":"10.1134/s003744662403008x","DOIUrl":null,"url":null,"abstract":"<p>We introduce the notion of ITBM-constructive algebra, which is a generalization of the notion of constructive algebra,\nand study completions of such algebras.\nWe obtain some criterion for the existence of completions for metrized algebras\nand prove that each ITBM-constructive metrized algebra\nwhich has completion can be naturally extended to the ITBM-constructive\ncompletion. Using these results, we establish the existence of\nITBM-constructive presentations for some particular algebras.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ITBM-Constructive Completions of Algebras\",\"authors\":\"A. S. Morozov\",\"doi\":\"10.1134/s003744662403008x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We introduce the notion of ITBM-constructive algebra, which is a generalization of the notion of constructive algebra,\\nand study completions of such algebras.\\nWe obtain some criterion for the existence of completions for metrized algebras\\nand prove that each ITBM-constructive metrized algebra\\nwhich has completion can be naturally extended to the ITBM-constructive\\ncompletion. Using these results, we establish the existence of\\nITBM-constructive presentations for some particular algebras.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s003744662403008x\",\"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://doi.org/10.1134/s003744662403008x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce the notion of ITBM-constructive algebra, which is a generalization of the notion of constructive algebra,
and study completions of such algebras.
We obtain some criterion for the existence of completions for metrized algebras
and prove that each ITBM-constructive metrized algebra
which has completion can be naturally extended to the ITBM-constructive
completion. Using these results, we establish the existence of
ITBM-constructive presentations for some particular algebras.
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