TY - CHAP
T1 - b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings
AU - Filippis, Vincenzo De
AU - Scudo, Giovanni
AU - Wei, Feng
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid. In this paper we define b-generalized skew derivations of prime rings. Then we describe all possible forms of two b-generalized skew derivations F and G satisfying the condition F(x)x − xG(x) = 0, for all x ∈ S, where S is the set of the evaluations of a multilinear polynomial f(x1, …, xn) over C with n non-commuting variables. Several potential research topics related to our current work are also presented.
AB - Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid. In this paper we define b-generalized skew derivations of prime rings. Then we describe all possible forms of two b-generalized skew derivations F and G satisfying the condition F(x)x − xG(x) = 0, for all x ∈ S, where S is the set of the evaluations of a multilinear polynomial f(x1, …, xn) over C with n non-commuting variables. Several potential research topics related to our current work are also presented.
KW - Generalized skew derivations
KW - Multilinear polynomials
KW - Prime rings
UR - http://www.scopus.com/inward/record.url?scp=85103251559&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-63111-6_7
DO - 10.1007/978-3-030-63111-6_7
M3 - Chapter
AN - SCOPUS:85103251559
T3 - Springer INdAM Series
SP - 109
EP - 138
BT - Springer INdAM Series
PB - Springer-Verlag Italia s.r.l.
ER -