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

Neshtiman Nooraldeen Suliman

Discussiones Mathematicae - General Algebra and Applications (2015)

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

Abstract

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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.

How to cite

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Neshtiman 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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  1. [1] W.E. Barness, On the Γ-rings of Nobusawa, Pacific J. Math. 18 (3) (1966) 411-422. 
  2. [2] M. Bresar and J. Vukman, On some additive mappings in rings with involution, Aequation Math. 38 (1989) 178-185. doi: 10.1007/BF01840003 Zbl0691.16041
  3. [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. [4] S. Kyuno, On prime gamma rings, Pacific J. Math. 75 (1978) 185-190. Zbl0381.16022
  5. [5] L. Luh, On the theory of simple Gamma rings, Michigan Math. J. 16 (1969) 576-584. doi: 10.1307/mmj/1029000167 
  6. [6] N. Nobusawa, On a generalization of the ring theory, Osaka J. Math. 1 (1964) 81-89. Zbl0135.02701
  7. [7] M. Sapanci and A. Nakajima, A note on gamma rings, Turkish J. Math. 20 (1996) 463-465. 
  8. [8] M. Soytürk, The commutativity in prime gamma rings with Derivation, Turkish J. Math. 18 (1994) 149-155. Zbl0860.16039

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