Centralizing Mappings of Semiprime Rings

Bell, Howard E.; Martindale, Wallace S.

doi:10.4153/cmb-1987-014-x

Cited by 196 publications

(91 citation statements)

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“…Considerable work has been done on centralizing and commuting mappings (see, e.g., [2,3,8,9] and references therein). Derivations are generalized as a-or skew-derivations.…”

Section: (Xy) -Xd(y) + D(x)(y) For All Xy € R Let a G R Then The Mmentioning

confidence: 99%

A NOTE ON Α-Derivations ON SEMIPRIME RINGS

Thaheem¹,

Samman²

2001

Demonstratio Mathematica

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Abstract. In this note we investigate some properties of a-derivations on prime and semiprime rings. We establish some identities for a commuting a-derivation d on a semiprime ring R and show that d maps R into its center and obtain some well-known results as a consequence. We also generalize Posner's theorem on the composition of derivations for a-derivations and as an application resolve a functional equation of automorphisms on certain prime rings.

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“…Considerable work has been done on centralizing and commuting mappings (see, e.g., [2,3,8,9] and references therein). Derivations are generalized as a-or skew-derivations.…”

Section: (Xy) -Xd(y) + D(x)(y) For All Xy € R Let a G R Then The Mmentioning

confidence: 99%

A NOTE ON Α-Derivations ON SEMIPRIME RINGS

Thaheem¹,

Samman²

2001

Demonstratio Mathematica

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“…E. Bell and W. S. Martindale [2] studied centralizing endomorpnisms and centralizing derivations on semiprime rings. In fact they merely assumed that the mappings are centralizing on some nonzero one-sided ideal of a semiprime ring.…”

Section: Centralizing O-derivationsmentioning

confidence: 99%

“…J. Mayne [15] proved the analogous result for centralizing automorphisms on prime rings. A number of algebraists have extended these theorems of Posner and Mayne in several ways (see, e.g., [1,2,3,6,7,9,12,16,17]). There has also been some interest in centralizing mappings defined on Banach algebras.…”

Section: Introductionmentioning

confidence: 99%

Centralizing mappings on von Neumann algebras

Brešar¹

1991

Proc. Amer. Math. Soc.

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Let R R be a ring with center Z ( R ) Z(R) . A mapping F F of R R into itself is called centralizing if F ( x ) x − x F ( x ) ∈ Z ( R ) F(x)x - xF(x) \in Z(R) for all x ∈ R x \in R . The main result of this paper states that every additive centralizing mapping F F on a von Neumann algebra R R is of the form F ( x ) = c x + ζ ( x ) , x ∈ R F(x) = cx + \zeta (x),x \in R , where c ∈ Z ( R ) c \in Z(R) and ζ \zeta is an additive mapping from R R into Z ( R ) Z(R) . We also consider α \alpha -derivations and some related mappings, which are centralizing on rings and Banach algebras

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“…After this, many articles have contributed to the generalization of this result in various directions (see, for example, Beidar et al, 1996Beidar et al, , 2000Bell and Martindale, 1987;Brešar, 1993;Hongan, 1991;Lee and Lee, 1983;Lee, 2001;Mayne, 1984 and references contained within). Recently, there are articles published on prime (Lie) superalgebras (for example, Beidar et al, 2003;Fošner, 2004;Gómez-Ambrosi et al, 2000;Montgomery, 1997;Montaner, 1998) which make it natural to consider some version of Posner's Theorem for superderivations on prime superalgebras.…”

Section: Introductionmentioning

confidence: 98%