Derivation Requirements on Prime Near-Rings for Commutative Rings
DOI:
https://doi.org/10.19184/jid.v20i2.10297Abstract
Near-ring is an extension of ring without having to fulfill a commutative of the addition operations and left distributive of the addition and multiplication operations It has been found that some theorems related to a prime near-rings are commutative rings involving the derivation of the Lie products and the derivation of the Jordan product. The contribution of this paper is developing the previous theorem by inserting derivations to the Lie products and the Jordan product.
Keywords: Derivation, Prime Near-Ring, Lie Products and Jordan Products.
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References
Argac, N & Bell. H. E. 2001. Some Results on Derivations in Near-rings. Near-Rings and Near-Fields : 42–46.
Bell, H. E. & Mason, G. 1987. On Derivations in Near-Rings North-Holland Math. Stud. 37 : 31–35.
Bell, H. E. & Mason, G. 1997. On Derivations in Near-Rings, II. Near-rings, Nearfields and K-Loops.: 191–197
Argac, N & Bell. H. E. 2001. Some Results on Derivations in Nearrings. Near-Rings and Near-Fields: 42–46.
Bell, H. E. & Mason, G. 1987. On Derivations in Near-Rings North-Holland Math. Stud. 37:31–35.
Bell, H. E. & Mason, G. 1997. On Derivations in Near-Rings, II.Near-rings, Nearfields and K-Loops: 191–197
Gotmare, A. R. 2016. Derivations in Prime Near Rings. Int. J. Pure Engg. Math. 4:101-105.
Kamal, A. A. M & Al-Shaalan, K. H. 2013. Existence of Derivations on Near-Rings.Math. Slovaca. 63:431-448
Kamal, A. A. M & Al-Shaalan, K. H. 2014. Commutativity of Near-rings with Derivations. Algebr. Colloq.21:215-230
Pilz, G. 1983. Near-Rings the Theory and its Applications. Amsterdam: North-Holland Publishing Company
Shang, Y. 2011. A Study of Derivations in Prime Near-Rings. Math. Balk. 25:413-417.
Bell, H. E. & Mason, G. 1987. On Derivations in Near-Rings North-Holland Math. Stud. 37 : 31–35.
Bell, H. E. & Mason, G. 1997. On Derivations in Near-Rings, II. Near-rings, Nearfields and K-Loops.: 191–197
Argac, N & Bell. H. E. 2001. Some Results on Derivations in Nearrings. Near-Rings and Near-Fields: 42–46.
Bell, H. E. & Mason, G. 1987. On Derivations in Near-Rings North-Holland Math. Stud. 37:31–35.
Bell, H. E. & Mason, G. 1997. On Derivations in Near-Rings, II.Near-rings, Nearfields and K-Loops: 191–197
Gotmare, A. R. 2016. Derivations in Prime Near Rings. Int. J. Pure Engg. Math. 4:101-105.
Kamal, A. A. M & Al-Shaalan, K. H. 2013. Existence of Derivations on Near-Rings.Math. Slovaca. 63:431-448
Kamal, A. A. M & Al-Shaalan, K. H. 2014. Commutativity of Near-rings with Derivations. Algebr. Colloq.21:215-230
Pilz, G. 1983. Near-Rings the Theory and its Applications. Amsterdam: North-Holland Publishing Company
Shang, Y. 2011. A Study of Derivations in Prime Near-Rings. Math. Balk. 25:413-417.
