与具有亨塞尔值的有限维划分代数相关的范畴中的对象的同构问题

Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series Pub Date : 2024-01-04 DOI:10.29235/1561-2430-2023-59-4-271-278

V. Yanchevskiĭ

{"title":"与具有亨塞尔值的有限维划分代数相关的范畴中的对象的同构问题","authors":"V. Yanchevskiĭ","doi":"10.29235/1561-2430-2023-59-4-271-278","DOIUrl":null,"url":null,"abstract":"Abstract. Let K be a field. In this paper, we found the necessary and sufficient conditions for K-homomorphisms of noncommutative finite-dimensional central division K-algebras with henselian valuations being K-isomorphisms. A similar result is obtained for the case of algebras with involutions. A category interpretation of these results is given.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"29 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An isomorphism problem for objects in categories related to finite dimensional division algebras having henselian valuations\",\"authors\":\"V. Yanchevskiĭ\",\"doi\":\"10.29235/1561-2430-2023-59-4-271-278\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. Let K be a field. In this paper, we found the necessary and sufficient conditions for K-homomorphisms of noncommutative finite-dimensional central division K-algebras with henselian valuations being K-isomorphisms. A similar result is obtained for the case of algebras with involutions. A category interpretation of these results is given.\",\"PeriodicalId\":516297,\"journal\":{\"name\":\"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series\",\"volume\":\"29 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29235/1561-2430-2023-59-4-271-278\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29235/1561-2430-2023-59-4-271-278","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

摘要设 K 是一个域。在本文中，我们发现了非交换有限维中心划分 K 布尔的 K 同构为 K 同构的必要条件和充分条件。对于有卷积的数组，也得到了类似的结果。本文给出了这些结果的范畴解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An isomorphism problem for objects in categories related to finite dimensional division algebras having henselian valuations

Abstract. Let K be a field. In this paper, we found the necessary and sufficient conditions for K-homomorphisms of noncommutative finite-dimensional central division K-algebras with henselian valuations being K-isomorphisms. A similar result is obtained for the case of algebras with involutions. A category interpretation of these results is given.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

CiteScore

0.50

自引率

0.00%

发文量