On zero-power valued homoderivations in 3-prime near-rings
DOI:
https://doi.org/10.5269/bspm.62741Resumen
We will start this article by proving a crucial concept, which will allow us to overcome a set of obstacles we encountered in previous articles concerning the commutativity of near-ring involving homoderivations and Jordan ideals. Furthermore, we present examples to show that limitations imposed in the hypothesis of our results are necessary.
Referencias
1. E. F. Al harfie & N Muthana, On homoderivations and commutativity of prime rings, Bull. Soc. Math. Banja Luka, 9 (2019), 301-304.
2. A. Al-Kenani, A. Melaibari & N Muthana, Homoderivations and commutativity of ∗-prime rings, East-West J. Math., 2 (2015), 117-126.
3. H. E. Bell, On derivations in near-rings, II, Kluwer Acad. Publ., 426 (1997), 191-197. https://doi.org/10.1007/978-94-009-1481-0_10
4. A. Boua, Homoderivations and Jordan right ideals in 3-prime near-rings, AIP Conf. Proc. 2074, 020010-1-020010-8 (2019). https://doi.org/10.1063/1.5090627
5. A. Boua, L. Oukhtite, A. Raji, Jordan ideals and derivations in prime near-rings, Comment. Math. Univ. Carolin., 55 (2) (2014), 131-139.
6. A. Boua, Commutativity of near-rings with certain constrains on Jordan ideals, Bol. Soc. Paran. Mat. 36 (4) (2018), 159-170. https://doi.org/10.5269/bspm.v36i4.32032
7. A. Boua, Commutativity of Jordan ideals in 3-prime near-rings with derivations, Com. Korean Math. Soc. 33 (1) (2018), 37-44.
8. A. Boua and A. A. M. Kamal, Lie ideals and Jordan ideals in 3-prime near rings with derivations, JP J. Algebra Number Theory Appl. 37 (2015), 167-184. https://doi.org/10.17654/JPANTAOct2015_167_184
9. A. Boua and H. E. Bell, Jordan ideals and derivations satisfying algebraic identities, Bull. Iranian Math. Soc., 44 (2018), 1543-1554. https://doi.org/10.1007/s41980-018-0106-x
10. A. Boua, A. Ali and Ul. Huque, Several Algebraic Identities in 3-Prime Near-ring, Kragujevac J. Math., 42 (2) 2018, 249-258. https://doi.org/10.5937/KgJMath1802249B
11. M. M. El Sofy, Rings with some kinds of mappings, M. Sc. Thesis, Cairo University, Branch of Fayoum, (2000).
12. A. En-guady, A. Boua and E. Farhan, Some functional identities on near-rings involving Jordan ideals and left generalized derivations. Iraqi Journal of science, 62 (6) (2021), 1961-1967. https://doi.org/10.24996/ijs.2021.62.6.21
13. A. Melaibari, N. Muthana & A. Al-Kenani, Homoderivations on Rings, Gen. Math. Notes, 1 (2016), 1-8. https://doi.org/10.56947/gjom.v4i2.67
14. S. Mouhssine and A. Boua, Homoderivations and semigroup ideals in 3-prime near-rings. Alg. Struc. App., 8 (2) (2021), 177-194.
2. A. Al-Kenani, A. Melaibari & N Muthana, Homoderivations and commutativity of ∗-prime rings, East-West J. Math., 2 (2015), 117-126.
3. H. E. Bell, On derivations in near-rings, II, Kluwer Acad. Publ., 426 (1997), 191-197. https://doi.org/10.1007/978-94-009-1481-0_10
4. A. Boua, Homoderivations and Jordan right ideals in 3-prime near-rings, AIP Conf. Proc. 2074, 020010-1-020010-8 (2019). https://doi.org/10.1063/1.5090627
5. A. Boua, L. Oukhtite, A. Raji, Jordan ideals and derivations in prime near-rings, Comment. Math. Univ. Carolin., 55 (2) (2014), 131-139.
6. A. Boua, Commutativity of near-rings with certain constrains on Jordan ideals, Bol. Soc. Paran. Mat. 36 (4) (2018), 159-170. https://doi.org/10.5269/bspm.v36i4.32032
7. A. Boua, Commutativity of Jordan ideals in 3-prime near-rings with derivations, Com. Korean Math. Soc. 33 (1) (2018), 37-44.
8. A. Boua and A. A. M. Kamal, Lie ideals and Jordan ideals in 3-prime near rings with derivations, JP J. Algebra Number Theory Appl. 37 (2015), 167-184. https://doi.org/10.17654/JPANTAOct2015_167_184
9. A. Boua and H. E. Bell, Jordan ideals and derivations satisfying algebraic identities, Bull. Iranian Math. Soc., 44 (2018), 1543-1554. https://doi.org/10.1007/s41980-018-0106-x
10. A. Boua, A. Ali and Ul. Huque, Several Algebraic Identities in 3-Prime Near-ring, Kragujevac J. Math., 42 (2) 2018, 249-258. https://doi.org/10.5937/KgJMath1802249B
11. M. M. El Sofy, Rings with some kinds of mappings, M. Sc. Thesis, Cairo University, Branch of Fayoum, (2000).
12. A. En-guady, A. Boua and E. Farhan, Some functional identities on near-rings involving Jordan ideals and left generalized derivations. Iraqi Journal of science, 62 (6) (2021), 1961-1967. https://doi.org/10.24996/ijs.2021.62.6.21
13. A. Melaibari, N. Muthana & A. Al-Kenani, Homoderivations on Rings, Gen. Math. Notes, 1 (2016), 1-8. https://doi.org/10.56947/gjom.v4i2.67
14. S. Mouhssine and A. Boua, Homoderivations and semigroup ideals in 3-prime near-rings. Alg. Struc. App., 8 (2) (2021), 177-194.
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2022-12-27
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