{"title":"具有中心扩展高阶$$*$$-导数的环","authors":"O. H. Ezzat","doi":"10.1007/s00006-023-01265-z","DOIUrl":null,"url":null,"abstract":"<div><p>We study the notions of centrally-extended higher <span>\\(*\\)</span>-derivations and centrally-extended generalized higher <span>\\(*\\)</span>-derivations. Both are shown to be additive in a <span>\\(*\\)</span>-ring without nonzero central ideals. Also, we prove that in semiprime <span>\\(*\\)</span>-rings with no nonzero central ideals, every centrally-extended (generalized) higher <span>\\(*\\)</span>-derivation is a (generalized) higher <span>\\(*\\)</span>-derivation.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 2","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rings with Centrally-Extended Higher \\\\(*\\\\)-Derivations\",\"authors\":\"O. H. Ezzat\",\"doi\":\"10.1007/s00006-023-01265-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the notions of centrally-extended higher <span>\\\\(*\\\\)</span>-derivations and centrally-extended generalized higher <span>\\\\(*\\\\)</span>-derivations. Both are shown to be additive in a <span>\\\\(*\\\\)</span>-ring without nonzero central ideals. Also, we prove that in semiprime <span>\\\\(*\\\\)</span>-rings with no nonzero central ideals, every centrally-extended (generalized) higher <span>\\\\(*\\\\)</span>-derivation is a (generalized) higher <span>\\\\(*\\\\)</span>-derivation.</p></div>\",\"PeriodicalId\":7330,\"journal\":{\"name\":\"Advances in Applied Clifford Algebras\",\"volume\":\"33 2\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Clifford Algebras\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00006-023-01265-z\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-023-01265-z","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Rings with Centrally-Extended Higher \(*\)-Derivations
We study the notions of centrally-extended higher \(*\)-derivations and centrally-extended generalized higher \(*\)-derivations. Both are shown to be additive in a \(*\)-ring without nonzero central ideals. Also, we prove that in semiprime \(*\)-rings with no nonzero central ideals, every centrally-extended (generalized) higher \(*\)-derivation is a (generalized) higher \(*\)-derivation.
期刊介绍：
Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.
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