{"title":"环同态","authors":"J. Gallian","doi":"10.1142/9789814271905_0014","DOIUrl":null,"url":null,"abstract":"• If R and S are ring, a function f : R → S is a ring homomorphism (or a ring map) if f (x + y) = f (x) + f (y) and f (xy) = f (x)f (y) for all x, y ∈ R. If R and S are rings with identity, it's customary to also require that f (1) = 1.","PeriodicalId":213836,"journal":{"name":"Contemporary Abstract Algebra","volume":"295 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Ring Homomorphisms\",\"authors\":\"J. Gallian\",\"doi\":\"10.1142/9789814271905_0014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"• If R and S are ring, a function f : R → S is a ring homomorphism (or a ring map) if f (x + y) = f (x) + f (y) and f (xy) = f (x)f (y) for all x, y ∈ R. If R and S are rings with identity, it's customary to also require that f (1) = 1.\",\"PeriodicalId\":213836,\"journal\":{\"name\":\"Contemporary Abstract Algebra\",\"volume\":\"295 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Contemporary Abstract Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789814271905_0014\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Contemporary Abstract Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789814271905_0014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
•如果R和S是环，则函数f: R→S是环同态(或环映射)，如果f (x + y) = f (x) + f (y)和f (xy) = f (x)f (y)对于所有x, y∈R。如果R和S是具有恒等的环，习惯上也要求f(1) = 1。
• If R and S are ring, a function f : R → S is a ring homomorphism (or a ring map) if f (x + y) = f (x) + f (y) and f (xy) = f (x)f (y) for all x, y ∈ R. If R and S are rings with identity, it's customary to also require that f (1) = 1.
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