{"title":"素环中广义衍生的乔丹同源行为","authors":"Nripendu Bera, Basudeb Dhara","doi":"10.1007/s11253-024-02265-3","DOIUrl":null,"url":null,"abstract":"<p>Suppose that <i>R</i> is a prime ring with char(<i>R</i>) <i>≠</i> 2 and <i>f</i>(ξ<sub>1</sub><i>, . . . ,</i> ξ<sub><i>n</i></sub>) is a noncentral multilinear polynomial over <i>C</i>(= <i>Z</i>(<i>U</i>))<i>,</i> where <i>U</i> is the Utumi quotient ring of <i>R.</i> An additive mapping <i>h</i> : <i>R</i> ⟶<i> R</i> is called homoderivation if <i>h</i>(<i>ab</i>) = <i>h</i>(<i>a</i>)<i>h</i>(<i>b</i>)+<i>h</i>(<i>a</i>)<i>b</i>+<i>ah</i>(<i>b</i>) for all <i>a, b</i> ∈ <i>R.</i> We investigate the behavior of three generalized derivations <i>F, G,</i> and <i>H</i> of <i>R</i> satisfying the condition</p><p><span>\\(F\\left({\\xi }^{2}\\right)=G\\left({\\xi }^{2}\\right)+H\\left(\\xi \\right)\\xi +\\xi H\\left(\\xi \\right)\\)</span></p><p>for all ξ ∈<i> f</i>(<i>R</i>) = {<i>f</i>(ξ<sub>1</sub><i>, . . . ,</i> ξ<sub><i>n</i></sub>) <i>|</i> ξ<sub>1</sub><i>, . . . ,</i> ξ<sub><i>n</i></sub> ∈<i> R</i>}<i>.</i></p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"33 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Jordan Homoderivation Behavior of Generalized Derivations in Prime Rings\",\"authors\":\"Nripendu Bera, Basudeb Dhara\",\"doi\":\"10.1007/s11253-024-02265-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Suppose that <i>R</i> is a prime ring with char(<i>R</i>) <i>≠</i> 2 and <i>f</i>(ξ<sub>1</sub><i>, . . . ,</i> ξ<sub><i>n</i></sub>) is a noncentral multilinear polynomial over <i>C</i>(= <i>Z</i>(<i>U</i>))<i>,</i> where <i>U</i> is the Utumi quotient ring of <i>R.</i> An additive mapping <i>h</i> : <i>R</i> ⟶<i> R</i> is called homoderivation if <i>h</i>(<i>ab</i>) = <i>h</i>(<i>a</i>)<i>h</i>(<i>b</i>)+<i>h</i>(<i>a</i>)<i>b</i>+<i>ah</i>(<i>b</i>) for all <i>a, b</i> ∈ <i>R.</i> We investigate the behavior of three generalized derivations <i>F, G,</i> and <i>H</i> of <i>R</i> satisfying the condition</p><p><span>\\\\(F\\\\left({\\\\xi }^{2}\\\\right)=G\\\\left({\\\\xi }^{2}\\\\right)+H\\\\left(\\\\xi \\\\right)\\\\xi +\\\\xi H\\\\left(\\\\xi \\\\right)\\\\)</span></p><p>for all ξ ∈<i> f</i>(<i>R</i>) = {<i>f</i>(ξ<sub>1</sub><i>, . . . ,</i> ξ<sub><i>n</i></sub>) <i>|</i> ξ<sub>1</sub><i>, . . . ,</i> ξ<sub><i>n</i></sub> ∈<i> R</i>}<i>.</i></p>\",\"PeriodicalId\":49406,\"journal\":{\"name\":\"Ukrainian Mathematical Journal\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ukrainian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11253-024-02265-3\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ukrainian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02265-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
假设 R 是质环,char(R) ≠ 2,f(ξ1, ... , ξn) 是 C(= Z(U))上的非中心多线性多项式,其中 U 是 R 的乌图米商环。如果对于所有 a, b∈ R,h(ab) = h(a)h(b)+h(a)b+ah(b) ,则加法映射 h : R ⟶ R 称为同化。对于所有ξ∈ f(R) = {f(ξ1,., ξn) | ξ1, ., ξn∈ R}。
Jordan Homoderivation Behavior of Generalized Derivations in Prime Rings
Suppose that R is a prime ring with char(R) ≠ 2 and f(ξ1, . . . , ξn) is a noncentral multilinear polynomial over C(= Z(U)), where U is the Utumi quotient ring of R. An additive mapping h : R ⟶ R is called homoderivation if h(ab) = h(a)h(b)+h(a)b+ah(b) for all a, b ∈ R. We investigate the behavior of three generalized derivations F, G, and H of R satisfying the condition
期刊介绍:
Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries.
Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.