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
DOC. TYPE
Article
ABSTRACT
Let â„› and \$\${\fancyscript S}\$\$ be arbitrary associative rings. A mapping Ï† of â„› onto \$\${\fancyscript S}\$\$ is called a multiplicative isomorphism if Ï† is bijective and satisfies Ï†( xy) = Ï†( x)Ï†( y) for all x, y âˆˆ â„›. In this short note, we establish a condition on â„›, in the case where â„› may not contain any nonâ€“zero idempotents, that assures that Ï† 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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