IJPAM: Volume 70, No. 7 (2011)
ON MULTILINEAR POLYNOMIALS IN
PRIME RINGS WITH DERIVATIONS
PRIME RINGS WITH DERIVATIONS
Basudeb Dhara
, Deepankar Das
Department of Mathematics
Belda College
Belda, Paschim Medinipur, 721424, W.B., INDIA
Department of Mathematics
Haldia Goverment College
Haldia, Purba Medinipur, 721657. W.B., INDIA



Belda College
Belda, Paschim Medinipur, 721424, W.B., INDIA

Haldia Goverment College
Haldia, Purba Medinipur, 721657. W.B., INDIA
Abstract. Let be a prime ring with extended centroid
and
characteristic different from
,
a nonzero derivation of
,
a nonzero multilinear polynomial over
and
a nonzero right ideal of
. If the mapping
is centralizing on
, then one of the following holds:
(1) is inner derivation induced by an element
such that
;
(2)
is an identity for
.
Received: April 3, 2011
AMS Subject Classification: 16W25, 16R50, 16N60
Key Words and Phrases: prime ring, derivation, extended centroid, Martindale quotient ring
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 7