{"title":"作用于对合环上的乘法广义逆* ce导数","authors":"A. M. Khaled, A. Ghareeb, M. El-Sayiad","doi":"10.1155/2023/2102909","DOIUrl":null,"url":null,"abstract":"<jats:p>Let <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <mi>S</mi>\n </math>\n </jats:inline-formula> be a ring with involution having a nontrivial symmetric idempotent element <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <mi>e</mi>\n </math>\n </jats:inline-formula>. If <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\n <mi mathvariant=\"normal\">Ω</mi>\n </math>\n </jats:inline-formula> is any appropriate multiplicative generalized reverse <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\n <msup>\n <mtext> </mtext>\n <mi>∗</mi>\n </msup>\n </math>\n </jats:inline-formula>CE-derivation of <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\n <mi>S</mi>\n </math>\n </jats:inline-formula> with involution <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\n <mi>∗</mi>\n </math>\n </jats:inline-formula>, then under some suitable restrictions on <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\n <mi>S</mi>\n </math>\n </jats:inline-formula>, <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\">\n <mi mathvariant=\"normal\">Ω</mi>\n </math>\n </jats:inline-formula> is centrally-extended additive.</jats:p>","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multiplicative Generalized Reverse <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <msup>\\n <mrow />\\n <mi>∗</mi>\\n </msup>\\n </math>CE-Derivations Acting on Rings with Involution\",\"authors\":\"A. M. Khaled, A. Ghareeb, M. El-Sayiad\",\"doi\":\"10.1155/2023/2102909\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<jats:p>Let <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <mi>S</mi>\\n </math>\\n </jats:inline-formula> be a ring with involution having a nontrivial symmetric idempotent element <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M3\\\">\\n <mi>e</mi>\\n </math>\\n </jats:inline-formula>. If <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M4\\\">\\n <mi mathvariant=\\\"normal\\\">Ω</mi>\\n </math>\\n </jats:inline-formula> is any appropriate multiplicative generalized reverse <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M5\\\">\\n <msup>\\n <mtext> </mtext>\\n <mi>∗</mi>\\n </msup>\\n </math>\\n </jats:inline-formula>CE-derivation of <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M6\\\">\\n <mi>S</mi>\\n </math>\\n </jats:inline-formula> with involution <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M7\\\">\\n <mi>∗</mi>\\n </math>\\n </jats:inline-formula>, then under some suitable restrictions on <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M8\\\">\\n <mi>S</mi>\\n </math>\\n </jats:inline-formula>, <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M9\\\">\\n <mi mathvariant=\\\"normal\\\">Ω</mi>\\n </math>\\n </jats:inline-formula> is centrally-extended additive.</jats:p>\",\"PeriodicalId\":43667,\"journal\":{\"name\":\"Muenster Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Muenster Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2023/2102909\",\"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":"Muenster Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2023/2102909","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Multiplicative Generalized Reverse CE-Derivations Acting on Rings with Involution
Let be a ring with involution having a nontrivial symmetric idempotent element . If is any appropriate multiplicative generalized reverse CE-derivation of with involution , then under some suitable restrictions on , is centrally-extended additive.
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