On commutativity of prime near-rings with multiplicative generalized derivation

Zeliha Bedir; Öznur Gölbaşı

doi:10.31801/cfsuasmas.443732

Research Article

Year 2019, Volume: 68 Issue: 1, 209 - 221, 01.02.2019

Zeliha Bedir Öznur Gölbaşı

https://doi.org/10.31801/cfsuasmas.443732

Abstract

References

Bell, H. and Mason, G., On derivations in near rings, Near rings and Near fields, North-Holland Mathematical Studies, 137, (1987), 31-35.
Bell, H. E., On derivations in near-rings II, Kluwer Academic Pub. Math. Appl., Dordr., 426, (1997), 191-197.
Daif, M. N., When is a multiplicative derivation additive, Int. J. Math. Math. Sci., 14 (3), (1991), 615-618.
Daif, M. N. , Bell, H. E., Remarks on derivations on semiprime rings, Int. J. Math. Math. Sci., 15(1), (1992), 205-206.
Daif, M. N. and Tammam El-Sayiad, M. S., Multiplicative generalized derivations which are additive, East-west J. Math., 9 (1), (2007), 31-37.
Bedir, Z., Gölbaşı, Ö., Notes on prime near rings with multiplicative derivation, Cumhuriyet University Faculty of Science, Science Journal (CSJ), (2017), Vol. 38, No. 2, 355-363.
Goldman, H. and Semrl, P., Multiplicative derivations on C(X), Monatsh Math., 121 (3), (1969), 189-197.
Kamal, A. M. and Al-Shaalan, K. H., Existence of derivations on near-rings, Math. Slovaca, 63, (2013), No:3, 431-438.
Martindale III, W. S., When are multiplicative maps additive, Proc. Amer. Math. Soc., 21, (1969), 695-698.
Pilz, G., Near-rings, 2nd Ed. North Holland, Amsterdam, (1983).

On commutativity of prime near-rings with multiplicative generalized derivation

Year 2019, Volume: 68 Issue: 1, 209 - 221, 01.02.2019

Zeliha Bedir Öznur Gölbaşı

https://doi.org/10.31801/cfsuasmas.443732

Abstract

In the present paper, we shall prove that 3-prime near-ring N is commutative ring, if any one of the following conditions are satisfied: (i) f(N)⊆Z, (ii) f([x,y])=0, (iii) f([x,y])=±[x,y], (iv) f([x,y])=±(xoy), (v) f([x,y])=[f(x),y], (vi) f([x,y])=[x,f(y)], (vii) f([x,y])=[d(x),y], (viii) f([x,y])=d(x)oy,(ix) [f(x),y]∈Z for all x,y∈N where f is a nonzero multiplicative generalized derivation of N associated with a multiplicative derivation d.

Keywords

Prime near-ring, derivation, multiplicative generalized derivation

References

Bell, H. and Mason, G., On derivations in near rings, Near rings and Near fields, North-Holland Mathematical Studies, 137, (1987), 31-35.
Bell, H. E., On derivations in near-rings II, Kluwer Academic Pub. Math. Appl., Dordr., 426, (1997), 191-197.
Daif, M. N., When is a multiplicative derivation additive, Int. J. Math. Math. Sci., 14 (3), (1991), 615-618.
Daif, M. N. , Bell, H. E., Remarks on derivations on semiprime rings, Int. J. Math. Math. Sci., 15(1), (1992), 205-206.
Daif, M. N. and Tammam El-Sayiad, M. S., Multiplicative generalized derivations which are additive, East-west J. Math., 9 (1), (2007), 31-37.
Bedir, Z., Gölbaşı, Ö., Notes on prime near rings with multiplicative derivation, Cumhuriyet University Faculty of Science, Science Journal (CSJ), (2017), Vol. 38, No. 2, 355-363.
Goldman, H. and Semrl, P., Multiplicative derivations on C(X), Monatsh Math., 121 (3), (1969), 189-197.
Kamal, A. M. and Al-Shaalan, K. H., Existence of derivations on near-rings, Math. Slovaca, 63, (2013), No:3, 431-438.
Martindale III, W. S., When are multiplicative maps additive, Proc. Amer. Math. Soc., 21, (1969), 695-698.
Pilz, G., Near-rings, 2nd Ed. North Holland, Amsterdam, (1983).

There are 10 citations in total.

Details

Primary Language	English
Journal Section	Review Articles
Authors	Zeliha Bedir Öznur Gölbaşı
Publication Date	February 1, 2019
Submission Date	June 16, 2017
Acceptance Date	November 28, 2017
Published in Issue	Year 2019 Volume: 68 Issue: 1

Cite

APA	Bedir, Z., & Gölbaşı, Ö. (2019). On commutativity of prime near-rings with multiplicative generalized derivation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 209-221. https://doi.org/10.31801/cfsuasmas.443732
AMA	Bedir Z, Gölbaşı Ö. On commutativity of prime near-rings with multiplicative generalized derivation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):209-221. doi:10.31801/cfsuasmas.443732
Chicago	Bedir, Zeliha, and Öznur Gölbaşı. “On Commutativity of Prime Near-Rings With Multiplicative Generalized Derivation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 209-21. https://doi.org/10.31801/cfsuasmas.443732.
EndNote	Bedir Z, Gölbaşı Ö (February 1, 2019) On commutativity of prime near-rings with multiplicative generalized derivation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 209–221.
IEEE	Z. Bedir and Ö. Gölbaşı, “On commutativity of prime near-rings with multiplicative generalized derivation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 209–221, 2019, doi: 10.31801/cfsuasmas.443732.
ISNAD	Bedir, Zeliha - Gölbaşı, Öznur. “On Commutativity of Prime Near-Rings With Multiplicative Generalized Derivation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 209-221. https://doi.org/10.31801/cfsuasmas.443732.
JAMA	Bedir Z, Gölbaşı Ö. On commutativity of prime near-rings with multiplicative generalized derivation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:209–221.
MLA	Bedir, Zeliha and Öznur Gölbaşı. “On Commutativity of Prime Near-Rings With Multiplicative Generalized Derivation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 209-21, doi:10.31801/cfsuasmas.443732.
Vancouver	Bedir Z, Gölbaşı Ö. On commutativity of prime near-rings with multiplicative generalized derivation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):209-21.