### NOTES ON LEFT IDEALS OF SEMIPRIME RINGS WITH MULTIPLICATIVE GENERALIZED (alpha,alpha)-DERIVATIONS

**DOI Number**

**First page**

**Last page**

#### Abstract

Let R be a 2-torsion free semiprime ring, I a nonzero left ideal

of R, alpha an automorphism on R and F a multiplicative (generalized)

(alpha,alpha)-derivation of R. This note we gave the description of commutativity of semiprime rings with help of some identities involving a multiplicative generalized (alpha,alpha)-derivation and a nonzero left ideal of R.

#### Keywords

#### Full Text:

PDF#### References

M. A. Ashraf, S. Ali and A. Ali: Some commutativity theorems for rings with generalized derivations. Southeast Asian Bull. Math. 31 (2007), 415-421.

M. Ashraf and N. Rehman: On derivations and commutativity in prime rings. East-West J. Math. 3(1) (2001), 87-91.

M. Bresar: On the distance of the compositions of two derivations to the generalized derivations. Glasgow Math. J. 33(1) (1991), 89-93.

M. N. Daif: When is a multiplicative derivation additive?. Int. J. Math. Math. Sci. 14(3) (1991), 615-618.

M. N. Daif and H. E. Bell: Remarks on derivations on semiprime rings. Int. J. Math. Math. Sci. 15(1) (1992), 205-206.

M. N. Daif and M. S. Tamman El-Sayiad: Multiplicative generalized derivation which are additive. East-West J. Math. 9(1) (1997), 31-37.

B. Dhara and S. Ali: On multiplicative (generalized) derivation in prime and semiprime rings. Aequat. Math. 86 (2013), 65-79.

B. Dhara, S. Ali and A. Pattanayak: Identities with generalized derivations in a semiprime rings. Demonstratio Mathematica. XLVI(3) (2013), 453-460.

B. Dhara, S. Kar and S. Kuila: A note on multiplicative (generalized) derivations and left ideals in semiprime rings. Rendiconti del Circolo Matematico di Palermo Series 2. DOI: 10.1007/s12215-020-00515-4.

H. Goldman and P. Semrl: Multiplicative derivations on C(X). Monatsh Math. 121(3) (1969), 189-197.

O. Golbasi: Multiplicative generalized derivations on ideals in semiprime rings. Math. Slovaca. 66(6) (2016), 1285-1296.

E. Koc and O. Golbasi: Multiplicative generalized derivations on Lie ideals in semiprime rings. Palastine Journal of Mathematics. 6 (2017), 219-227.

W. S. Martindale III: When are multiplicative maps additive?. Proc. Amer. Math. Soc. 21 (1969), 695-698.

M. A. Quadri, M. S. Khan and N. Rehman: Generalized derivations and commutativity of prime rings. Indian J. Pure Appl. Math. 34(9) (2003), 1393-1396.

DOI: https://doi.org/10.22190/FUMI210206067U

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)