求助PDF
{"title":"满足环中某些同一性的高阶衍生","authors":"Amal S. Alali, Shakir Ali, Naira N. Rafiquee, Vaishali Varshney","doi":"10.1155/2024/6550025","DOIUrl":null,"url":null,"abstract":"Let <svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 6.6501 6.1673\" width=\"6.6501pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> and <svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 10.3951 6.1673\" width=\"10.3951pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> be fixed positive integers. In this paper, we establish some structural properties of prime rings equipped with higher derivations. Motivated by the works of Herstein and Bell-Daif, we characterize rings with higher derivations <span><svg height=\"12.9265pt\" style=\"vertical-align:-3.63817pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 21.221 12.9265\" width=\"21.221pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,13.59,0)\"></path></g></svg><span></span><svg height=\"12.9265pt\" style=\"vertical-align:-3.63817pt\" version=\"1.1\" viewbox=\"24.803183800000003 -9.28833 34.147 12.9265\" width=\"34.147pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,24.853,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,29.351,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,36.501,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,39.557,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,44.055,3.132)\"><use xlink:href=\"#g50-106\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,46.603,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,51.891,3.132)\"></path></g></svg></span> satisfying (i) <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 36.037 12.7178\" width=\"36.037pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,4.485,0)\"><use xlink:href=\"#g113-101\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,11.635,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,16.81,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.308,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,28.575,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,33.073,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"38.1661838 -9.28833 46.507 12.7178\" width=\"46.507pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,38.216,0)\"><use xlink:href=\"#g113-101\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,45.366,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,53.217,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,57.715,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,65.244,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,69.742,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,77.859,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"88.30518380000001 -9.28833 30.722 12.7178\" width=\"30.722pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,88.355,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,97.351,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,101.849,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,114.121,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> for all <span><svg height=\"12.4438pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.01432 10.231 12.4438\" width=\"10.231pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.267,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"12.4438pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"12.3601838 -9.01432 18.025 12.4438\" width=\"18.025pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,12.41,0)\"><use xlink:href=\"#g113-122\"></use></g><g transform=\"matrix(.013,0,0,-0.013,23.571,0)\"><use xlink:href=\"#g117-173\"></use></g></svg><span></span><svg height=\"12.4438pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"34.0171838 -9.01432 12.508 12.4438\" width=\"12.508pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,34.067,0)\"><use xlink:href=\"#g198-19\"></use></g></svg></span> and (ii) <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 31.539 12.7178\" width=\"31.539pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-101\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,7.15,3.132)\"><use xlink:href=\"#g50-111\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.325,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,16.823,0)\"><use xlink:href=\"#g113-92\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.308,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,28.575,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"33.6681838 -9.28833 27.008 12.7178\" width=\"27.008pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,33.718,0)\"><use xlink:href=\"#g113-122\"></use></g><g transform=\"matrix(.013,0,0,-0.013,41.247,0)\"><use xlink:href=\"#g113-94\"></use></g><g transform=\"matrix(.013,0,0,-0.013,45.732,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,53.862,0)\"><use xlink:href=\"#g117-173\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"64.30818380000001 -9.28833 30.661 12.7178\" width=\"30.661pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,64.358,0)\"><use xlink:href=\"#g113-91\"></use></g><g transform=\"matrix(.013,0,0,-0.013,73.354,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,77.852,0)\"><use xlink:href=\"#g198-19\"></use></g><g transform=\"matrix(.013,0,0,-0.013,90.124,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> for all <span><svg height=\"12.4438pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.01432 10.231 12.4438\" width=\"10.231pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.267,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"12.4438pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"12.3601838 -9.01432 18.025 12.4438\" width=\"18.025pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,12.41,0)\"><use xlink:href=\"#g113-122\"></use></g><g transform=\"matrix(.013,0,0,-0.013,23.571,0)\"><use xlink:href=\"#g117-173\"></use></g></svg><span></span><span><svg height=\"12.4438pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"34.0171838 -9.01432 12.508 12.4438\" width=\"12.508pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,34.067,0)\"><use xlink:href=\"#g198-19\"></use></g></svg>.</span></span>","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"21 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Higher Derivations Satisfying Certain Identities in Rings\",\"authors\":\"Amal S. Alali, Shakir Ali, Naira N. Rafiquee, Vaishali Varshney\",\"doi\":\"10.1155/2024/6550025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <svg height=\\\"6.1673pt\\\" style=\\\"vertical-align:-0.2063904pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -5.96091 6.6501 6.1673\\\" width=\\\"6.6501pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g></svg> and <svg height=\\\"6.1673pt\\\" style=\\\"vertical-align:-0.2063904pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -5.96091 10.3951 6.1673\\\" width=\\\"10.3951pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g></svg> be fixed positive integers. In this paper, we establish some structural properties of prime rings equipped with higher derivations. Motivated by the works of Herstein and Bell-Daif, we characterize rings with higher derivations <span><svg height=\\\"12.9265pt\\\" style=\\\"vertical-align:-3.63817pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 21.221 12.9265\\\" width=\\\"21.221pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,13.59,0)\\\"></path></g></svg><span></span><svg height=\\\"12.9265pt\\\" style=\\\"vertical-align:-3.63817pt\\\" version=\\\"1.1\\\" viewbox=\\\"24.803183800000003 -9.28833 34.147 12.9265\\\" width=\\\"34.147pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,24.853,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,29.351,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,36.501,3.132)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,39.557,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,44.055,3.132)\\\"><use xlink:href=\\\"#g50-106\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,46.603,3.132)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,51.891,3.132)\\\"></path></g></svg></span> satisfying (i) <span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 36.037 12.7178\\\" width=\\\"36.037pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,4.485,0)\\\"><use xlink:href=\\\"#g113-101\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,11.635,3.132)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,16.81,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,21.308,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,28.575,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,33.073,0)\\\"></path></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"38.1661838 -9.28833 46.507 12.7178\\\" width=\\\"46.507pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,38.216,0)\\\"><use xlink:href=\\\"#g113-101\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,45.366,3.132)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,53.217,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,57.715,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,65.244,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,69.742,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,77.859,0)\\\"></path></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"88.30518380000001 -9.28833 30.722 12.7178\\\" width=\\\"30.722pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,88.355,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,97.351,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,101.849,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,114.121,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> for all <span><svg height=\\\"12.4438pt\\\" style=\\\"vertical-align:-3.42948pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.01432 10.231 12.4438\\\" width=\\\"10.231pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,7.267,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"12.4438pt\\\" style=\\\"vertical-align:-3.42948pt\\\" version=\\\"1.1\\\" viewbox=\\\"12.3601838 -9.01432 18.025 12.4438\\\" width=\\\"18.025pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,12.41,0)\\\"><use xlink:href=\\\"#g113-122\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,23.571,0)\\\"><use xlink:href=\\\"#g117-173\\\"></use></g></svg><span></span><svg height=\\\"12.4438pt\\\" style=\\\"vertical-align:-3.42948pt\\\" version=\\\"1.1\\\" viewbox=\\\"34.0171838 -9.01432 12.508 12.4438\\\" width=\\\"12.508pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,34.067,0)\\\"><use xlink:href=\\\"#g198-19\\\"></use></g></svg></span> and (ii) <span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 31.539 12.7178\\\" width=\\\"31.539pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-101\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,7.15,3.132)\\\"><use xlink:href=\\\"#g50-111\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,12.325,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,16.823,0)\\\"><use xlink:href=\\\"#g113-92\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,21.308,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,28.575,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"33.6681838 -9.28833 27.008 12.7178\\\" width=\\\"27.008pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,33.718,0)\\\"><use xlink:href=\\\"#g113-122\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,41.247,0)\\\"><use xlink:href=\\\"#g113-94\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,45.732,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,53.862,0)\\\"><use xlink:href=\\\"#g117-173\\\"></use></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"64.30818380000001 -9.28833 30.661 12.7178\\\" width=\\\"30.661pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,64.358,0)\\\"><use xlink:href=\\\"#g113-91\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,73.354,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,77.852,0)\\\"><use xlink:href=\\\"#g198-19\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,90.124,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> for all <span><svg height=\\\"12.4438pt\\\" style=\\\"vertical-align:-3.42948pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.01432 10.231 12.4438\\\" width=\\\"10.231pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,7.267,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"12.4438pt\\\" style=\\\"vertical-align:-3.42948pt\\\" version=\\\"1.1\\\" viewbox=\\\"12.3601838 -9.01432 18.025 12.4438\\\" width=\\\"18.025pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,12.41,0)\\\"><use xlink:href=\\\"#g113-122\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,23.571,0)\\\"><use xlink:href=\\\"#g117-173\\\"></use></g></svg><span></span><span><svg height=\\\"12.4438pt\\\" style=\\\"vertical-align:-3.42948pt\\\" version=\\\"1.1\\\" viewbox=\\\"34.0171838 -9.01432 12.508 12.4438\\\" width=\\\"12.508pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,34.067,0)\\\"><use xlink:href=\\\"#g198-19\\\"></use></g></svg>.</span></span>\",\"PeriodicalId\":54214,\"journal\":{\"name\":\"Journal of Mathematics\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-02-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1155/2024/6550025\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/6550025","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
引用
批量引用
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
