素环上的湮灭子条件和广义导数

Q2 Mathematics
B. Dhara, S. Kar, S. Ghosh
{"title":"素环上的湮灭子条件和广义导数","authors":"B. Dhara,&nbsp;S. Kar,&nbsp;S. Ghosh","doi":"10.1007/s11565-025-00597-x","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>R</i> be a prime ring with char <span>\\((R)\\ne 2\\)</span>, <i>I</i> be a nonzero ideal of <i>R</i>, <span>\\(f(x_1,\\ldots ,x_n)\\)</span> be a noncentral multilinear polynomial over extended centroid <i>C</i> and <span>\\(0\\ne b'\\in R\\)</span>. Denote <span>\\(f(I)=\\{f(t_1,\\ldots ,t_n) | t_1,\\ldots ,t_n\\in I\\}\\)</span>. Suppose that <i>F</i>, <i>G</i> and <i>H</i> are three generalized derivations on <i>R</i> such that </p><div><div><span>$$\\begin{aligned} b'\\Big \\{F\\Big (G(V)V\\Big )-H(V^2)\\Big \\}=0 \\end{aligned}$$</span></div></div><p>for all <span>\\(V\\in f(I)\\)</span>. Then the structure of the maps <i>F</i>, <i>G</i>, <i>H</i> are described. This result naturally generalizes the results obtained by Carini and De Filippis in [Siberian Math. J. 53 (6) (2012), 1051-1060], Dhara and Argac in [Commun. Math. Stat. 4 (2016), 39-54] and completes the incomplete result of Tiwari in [Rend. Circ. Mat. Palermo, II. Ser 71 (2022), 207-223]. At the end of this paper an example is given to show that the primeness condition is not superfluous.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2025-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Annihilator conditions and generalized derivations in prime rings\",\"authors\":\"B. Dhara,&nbsp;S. Kar,&nbsp;S. Ghosh\",\"doi\":\"10.1007/s11565-025-00597-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <i>R</i> be a prime ring with char <span>\\\\((R)\\\\ne 2\\\\)</span>, <i>I</i> be a nonzero ideal of <i>R</i>, <span>\\\\(f(x_1,\\\\ldots ,x_n)\\\\)</span> be a noncentral multilinear polynomial over extended centroid <i>C</i> and <span>\\\\(0\\\\ne b'\\\\in R\\\\)</span>. Denote <span>\\\\(f(I)=\\\\{f(t_1,\\\\ldots ,t_n) | t_1,\\\\ldots ,t_n\\\\in I\\\\}\\\\)</span>. Suppose that <i>F</i>, <i>G</i> and <i>H</i> are three generalized derivations on <i>R</i> such that </p><div><div><span>$$\\\\begin{aligned} b'\\\\Big \\\\{F\\\\Big (G(V)V\\\\Big )-H(V^2)\\\\Big \\\\}=0 \\\\end{aligned}$$</span></div></div><p>for all <span>\\\\(V\\\\in f(I)\\\\)</span>. Then the structure of the maps <i>F</i>, <i>G</i>, <i>H</i> are described. This result naturally generalizes the results obtained by Carini and De Filippis in [Siberian Math. J. 53 (6) (2012), 1051-1060], Dhara and Argac in [Commun. Math. Stat. 4 (2016), 39-54] and completes the incomplete result of Tiwari in [Rend. Circ. Mat. Palermo, II. Ser 71 (2022), 207-223]. At the end of this paper an example is given to show that the primeness condition is not superfluous.</p></div>\",\"PeriodicalId\":35009,\"journal\":{\"name\":\"Annali dell''Universita di Ferrara\",\"volume\":\"71 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2025-05-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali dell''Universita di Ferrara\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11565-025-00597-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali dell''Universita di Ferrara","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s11565-025-00597-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0

摘要

设R是带字符\((R)\ne 2\)的素环,I是R的非零理想,\(f(x_1,\ldots ,x_n)\)是扩展质心C和\(0\ne b'\in R\)上的非中心多线性多项式。表示\(f(I)=\{f(t_1,\ldots ,t_n) | t_1,\ldots ,t_n\in I\}\)。假设F, G和H是R的三个广义导数,使得$$\begin{aligned} b'\Big \{F\Big (G(V)V\Big )-H(V^2)\Big \}=0 \end{aligned}$$对于所有\(V\in f(I)\)。然后描述了映射F、G、H的结构。这个结果很自然地推广了卡里尼和德菲利皮斯在《西伯利亚数学》中得到的结果。[j] . [j] . 53 (6) (2012), 1051-1060 .]数学。统计,4(2016),39-54],完成了[Rend]中Tiwari的不完全结果。约马特。巴勒莫,二。[j].科学通报71(2022),207-223。最后给出了一个算例,说明素数条件不是多余的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Annihilator conditions and generalized derivations in prime rings

Let R be a prime ring with char \((R)\ne 2\), I be a nonzero ideal of R, \(f(x_1,\ldots ,x_n)\) be a noncentral multilinear polynomial over extended centroid C and \(0\ne b'\in R\). Denote \(f(I)=\{f(t_1,\ldots ,t_n) | t_1,\ldots ,t_n\in I\}\). Suppose that F, G and H are three generalized derivations on R such that

$$\begin{aligned} b'\Big \{F\Big (G(V)V\Big )-H(V^2)\Big \}=0 \end{aligned}$$

for all \(V\in f(I)\). Then the structure of the maps FGH are described. This result naturally generalizes the results obtained by Carini and De Filippis in [Siberian Math. J. 53 (6) (2012), 1051-1060], Dhara and Argac in [Commun. Math. Stat. 4 (2016), 39-54] and completes the incomplete result of Tiwari in [Rend. Circ. Mat. Palermo, II. Ser 71 (2022), 207-223]. At the end of this paper an example is given to show that the primeness condition is not superfluous.

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
Annali dell''Universita di Ferrara
Annali dell''Universita di Ferrara Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
71
期刊介绍: Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信