TITLE

Multiplicative Mappings of Rings

AUTHOR(S)
Fang Lu; Jin Xie
PUB. DATE
July 2006
SOURCE
Acta Mathematica Sinica;Jul2006, Vol. 22 Issue 4, p1017
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let ℛ and $${\fancyscript S}$$ be arbitrary associative rings. A mapping φ of ℛ onto $${\fancyscript S}$$ 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.
ACCESSION #
21690495

 

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