Multiplicative Mappings of Rings  

作　　者：Fang Yan LU Jin Hai XIE 

机构地区：[1]Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2006年第4期1017-1020,共4页数学学报（英文版）

基　　金：NNSFC(No.10571054);a grant(No.04KJB110116)from the government of Jiangsu Province of China

摘　　要：Let R and F be arbitrary associative rings. A mapping φ of R onto F is called a multiplicative isomorphism if φ is bijective and satisfies φ（xy） = φ（x）φ（y） for all x, y ∈ R. In this short note, we establish a condition on R, in the case where R may not contain any non-zero idempotents, that assures that φ is additive, which generalizes the famous Martindale＇s result. As an application, we show that under a mild assumption every multiplicative isomorphism from the radical of a nest algebra onto an arbitrary ring is additive.Let R and F be arbitrary associative rings. A mapping φ of R onto F is called a multiplicative isomorphism if φ is bijective and satisfies φ（xy） = φ（x）φ（y） for all x, y ∈ R. In this short note, we establish a condition on R, in the case where R may not contain any non-zero idempotents, that assures that φ is additive, which generalizes the famous Martindale＇s result. As an application, we show that under a mild assumption every multiplicative isomorphism from the radical of a nest algebra onto an arbitrary ring is additive.

关 键 词：Multiplicative isomorphisms ADDITIVITY IDEMPOTENTS 

分 类 号：O153.3[理学—数学]