# Some results of reverse derivation on prime and semiprime Γ-rings

Discussiones Mathematicae - General Algebra and Applications (2015)

- Volume: 35, Issue: 1, page 53-58
- ISSN: 1509-9415

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topNeshtiman Nooraldeen Suliman. "Some results of reverse derivation on prime and semiprime Γ-rings." Discussiones Mathematicae - General Algebra and Applications 35.1 (2015): 53-58. <http://eudml.org/doc/270152>.

@article{NeshtimanNooraldeenSuliman2015,

abstract = {In the present paper, it is introduced the definition of a reverse derivation on a Γ-ring M. It is shown that a mapping derivation on a semiprime Γ-ring M is central if and only if it is reverse derivation. Also it is shown that M is commutative if for all a,b ∈ I (I is an ideal of M) satisfying d(a) ∈ Z(M), and d(a ∘ b) = 0.},

author = {Neshtiman Nooraldeen Suliman},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {Prime Γ-rings; semiprime Γ-rings; derivations; reverse derivations},

language = {eng},

number = {1},

pages = {53-58},

title = {Some results of reverse derivation on prime and semiprime Γ-rings},

url = {http://eudml.org/doc/270152},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Neshtiman Nooraldeen Suliman

TI - Some results of reverse derivation on prime and semiprime Γ-rings

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2015

VL - 35

IS - 1

SP - 53

EP - 58

AB - In the present paper, it is introduced the definition of a reverse derivation on a Γ-ring M. It is shown that a mapping derivation on a semiprime Γ-ring M is central if and only if it is reverse derivation. Also it is shown that M is commutative if for all a,b ∈ I (I is an ideal of M) satisfying d(a) ∈ Z(M), and d(a ∘ b) = 0.

LA - eng

KW - Prime Γ-rings; semiprime Γ-rings; derivations; reverse derivations

UR - http://eudml.org/doc/270152

ER -

## References

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- [3] Md. F. Hoque and A.C. Paul, On centralizers of semiprime gamma rings, Intr. Math. Forum 6 (13) (2011) 627-638. Zbl1229.16044
- [4] S. Kyuno, On prime gamma rings, Pacific J. Math. 75 (1978) 185-190. Zbl0381.16022
- [5] L. Luh, On the theory of simple Gamma rings, Michigan Math. J. 16 (1969) 576-584. doi: 10.1307/mmj/1029000167
- [6] N. Nobusawa, On a generalization of the ring theory, Osaka J. Math. 1 (1964) 81-89. Zbl0135.02701
- [7] M. Sapanci and A. Nakajima, A note on gamma rings, Turkish J. Math. 20 (1996) 463-465.
- [8] M. Soytürk, The commutativity in prime gamma rings with Derivation, Turkish J. Math. 18 (1994) 149-155. Zbl0860.16039

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