{"title":"覆盖半素环上广义(alpha_1, alpha_2)导数的加性映射","authors":"F. Shujat, A. Ansari","doi":"10.56947/gjom.v11i2.495","DOIUrl":null,"url":null,"abstract":"Let R be a semiprime ring, (α1,α2) be automorphisms on R and Δ, δ be additive maps from R to R. If Δ and δ satisfying any one of the following identities:i) Δ(xnyn)=Δ(xn)α1(yn)+α2(xn)δ(yn)ii) Δ(xn)=Δ(xn-m)α1(xm)+α2(xn-m)δ(xm), for all x,y∈Rthen Δ will be generalized (α1,α2)-derivation with associated (α1,α2)-derivation on R.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Additive mappings covering generalized (alpha_1, alpha_2)-derivations in semiprime rings\",\"authors\":\"F. Shujat, A. Ansari\",\"doi\":\"10.56947/gjom.v11i2.495\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let R be a semiprime ring, (α1,α2) be automorphisms on R and Δ, δ be additive maps from R to R. If Δ and δ satisfying any one of the following identities:i) Δ(xnyn)=Δ(xn)α1(yn)+α2(xn)δ(yn)ii) Δ(xn)=Δ(xn-m)α1(xm)+α2(xn-m)δ(xm), for all x,y∈Rthen Δ will be generalized (α1,α2)-derivation with associated (α1,α2)-derivation on R.\",\"PeriodicalId\":421614,\"journal\":{\"name\":\"Gulf Journal of Mathematics\",\"volume\":\"5 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Gulf Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56947/gjom.v11i2.495\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gulf Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56947/gjom.v11i2.495","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Additive mappings covering generalized (alpha_1, alpha_2)-derivations in semiprime rings
Let R be a semiprime ring, (α1,α2) be automorphisms on R and Δ, δ be additive maps from R to R. If Δ and δ satisfying any one of the following identities:i) Δ(xnyn)=Δ(xn)α1(yn)+α2(xn)δ(yn)ii) Δ(xn)=Δ(xn-m)α1(xm)+α2(xn-m)δ(xm), for all x,y∈Rthen Δ will be generalized (α1,α2)-derivation with associated (α1,α2)-derivation on R.
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