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Generalized reverse derivations and commutativity of prime rings
- Source :
- Communications in Mathematics, Vol 27, Iss 1, Pp 43-50 (2019)
- Publication Year :
- 2019
- Publisher :
- episciences.org, 2019.
-
Abstract
- Let R be a prime ring with center Z(R) and I a nonzero right ideal of R. Suppose that R admits a generalized reverse derivation (F, d) such that d(Z(R)) ≠ 0. In the present paper, we shall prove that if one of the following conditions holds: (i) F (xy) ± xy ∈ Z(R) (ii) F ([x, y]) ± [F (x), y] ∈ Z(R) (iii) F ([x, y]) ± [F (x), F (y)] ∈ Z(R) (iv) F (x ο y) ± F (x) ο F (y) ∈ Z(R) (v) [F (x), y] ± [x, F (y)] ∈ Z(R) (vi) F (x) ο y ± x ο F (y) ∈ Z(R) for all x, y ∈ I, then R is commutative.
- Subjects :
- Physics
16n60
General Mathematics
010102 general mathematics
Center (category theory)
prime rings
01 natural sciences
Prime (order theory)
010101 applied mathematics
Combinatorics
generalized reverse derivations
reverse derivations
Prime ring
16w25
16a70
QA1-939
Ideal (ring theory)
0101 mathematics
[MATH]Mathematics [math]
Commutative property
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Communications in Mathematics, Vol 27, Iss 1, Pp 43-50 (2019)
- Accession number :
- edsair.doi.dedup.....3c17d69b4f2afa767cb0aff9c5422b2f