环和无差别群的嵌入原理

IF 1 Q1 MATHEMATICS

Formalized Mathematics Pub Date : 2023-09-01 DOI:10.2478/forma-2023-0013

Yasushige Watase

{"title":"环和无差别群的嵌入原理","authors":"Yasushige Watase","doi":"10.2478/forma-2023-0013","DOIUrl":null,"url":null,"abstract":"Summary The article concerns about formalizing a certain lemma on embedding of algebraic structures in the Mizar system, claiming that if a ring A is embedded in a ring B then there exists a ring C which is isomorphic to B and includes A as a subring. This construction applies to algebraic structures such as Abelian groups and rings.","PeriodicalId":42667,"journal":{"name":"Formalized Mathematics","volume":"6 1","pages":"143 - 150"},"PeriodicalIF":1.0000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Embedding Principle for Rings and Abelian Groups\",\"authors\":\"Yasushige Watase\",\"doi\":\"10.2478/forma-2023-0013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary The article concerns about formalizing a certain lemma on embedding of algebraic structures in the Mizar system, claiming that if a ring A is embedded in a ring B then there exists a ring C which is isomorphic to B and includes A as a subring. This construction applies to algebraic structures such as Abelian groups and rings.\",\"PeriodicalId\":42667,\"journal\":{\"name\":\"Formalized Mathematics\",\"volume\":\"6 1\",\"pages\":\"143 - 150\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Formalized Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/forma-2023-0013\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Formalized Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/forma-2023-0013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要文章关注在米扎（Mizar）系统中形式化关于代数结构嵌入的某个 Lemma，声称如果一个环 A 嵌入一个环 B，那么存在一个与 B 同构并包含 A 作为子环的环 C。这一构造适用于代数结构，如阿贝尔群和环。

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

Embedding Principle for Rings and Abelian Groups

Summary The article concerns about formalizing a certain lemma on embedding of algebraic structures in the Mizar system, claiming that if a ring A is embedded in a ring B then there exists a ring C which is isomorphic to B and includes A as a subring. This construction applies to algebraic structures such as Abelian groups and rings.

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

Formalized Mathematics MATHEMATICS-

自引率

0.00%

发文量

审稿时长

10 weeks

期刊介绍： Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.