{"title":"幂等一元代数的非线性反交换映射","authors":"Liqin Feng, X. Qi","doi":"10.12988/imf.2019.9524","DOIUrl":null,"url":null,"abstract":"Let A be a unital algebra with a nontrivial idempotent e1. A map φ : A → A is anti-commuting if [φ(a), b] = −[a, φ(b)] holds for all a, b ∈ A. In this paper, we give a general form of φ on A; particularly, if A is prime, then such maps are either central-valued maps or of the forms a 7→ za+ f(a) for all a ∈ A, where z is in the center of A and f is a central-valued map. Mathematics Subject Classification: 47B47, 47B49, 46L10","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Nonlinear anti-commuting maps of unital algebras with idempotents\",\"authors\":\"Liqin Feng, X. Qi\",\"doi\":\"10.12988/imf.2019.9524\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let A be a unital algebra with a nontrivial idempotent e1. A map φ : A → A is anti-commuting if [φ(a), b] = −[a, φ(b)] holds for all a, b ∈ A. In this paper, we give a general form of φ on A; particularly, if A is prime, then such maps are either central-valued maps or of the forms a 7→ za+ f(a) for all a ∈ A, where z is in the center of A and f is a central-valued map. Mathematics Subject Classification: 47B47, 47B49, 46L10\",\"PeriodicalId\":107214,\"journal\":{\"name\":\"International Mathematical Forum\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematical Forum\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/imf.2019.9524\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematical Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/imf.2019.9524","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Nonlinear anti-commuting maps of unital algebras with idempotents
Let A be a unital algebra with a nontrivial idempotent e1. A map φ : A → A is anti-commuting if [φ(a), b] = −[a, φ(b)] holds for all a, b ∈ A. In this paper, we give a general form of φ on A; particularly, if A is prime, then such maps are either central-valued maps or of the forms a 7→ za+ f(a) for all a ∈ A, where z is in the center of A and f is a central-valued map. Mathematics Subject Classification: 47B47, 47B49, 46L10
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