Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings

de Filippis, Vincenzo

doi:10.1007/s10587-016-0255-0

Geodesic

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Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings

de Filippis, Vincenzo

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 271-292.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

Let

R

be a prime ring of characteristic different from 2,

Q_{r}

its right Martindale quotient ring and

C

its extended centroid. Suppose that

F

G

are generalized skew derivations of

R

with the same associated automorphism

α

, and

p (x_{1}, \dots, x_{n})

is a non-central polynomial over

C

such that $$ [F(x),\alpha (y)]=G([x,y]) $$ for all

x, y \in {p (r_{1}, \dots, r_{n}) : r_{1}, \dots, r_{n} \in R}

. Then there exists

λ \in C

such that

F (x) = G (x) = λ α (x)

for all

x \in R

MR Zbl

DOI : 10.1007/s10587-016-0255-0

Classification : 16N60, 16W25
Mots-clés : generalized skew derivation; prime ring

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     title = {Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {271--292},
     publisher = {mathdoc},
     volume = {66},
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     year = {2016},
     doi = {10.1007/s10587-016-0255-0},
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     zbl = {06587889},
     language = {en},
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de Filippis, Vincenzo. Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 271-292. doi : 10.1007/s10587-016-0255-0. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0255-0/

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