Homoderivations and semigroup ideals in $3$-prime near-rings

Document Type : Research Paper

Authors

University Sidi Mohammed Ben Abdellah, Polydisciplinary Faculty, Department of Mathematics, Physics and Computer Science, LSI, Taza; Morocco.

10.29252/as.2021.2110

Abstract

This paper studies homoderivations satisfying certain conditions on semigroup ideals of near-rings. In addition, we include some examples of the necessity of the hypotheses used in our results.

Keywords


[1] E. F. Al harfie and N. Muthana, On homoderivations and commutativity of prime rings, Bull. int. math. virtual inst., 9 (2019) 301-304.
[2] A. Al-Kenani, A. Melaibari and N. Muthana, Homoderivations and commutativity of *-prime rings, East-West J. of Math., 17 No. 2 (2015) 117-126.
[3] H. E. Bell, On derivations in near-rings II, Kluwer Acad. Publ., 426 (1997) 191-197.
[4] H. E. Bell, A. Boua and L. Oukhtite, Semigroup ideals and commutativity in 3-prime near-rings, Comm. in Alg., 43 (2015) 1757-1770.
[5] A. Boua, A .Ali and I. Huque, Serval algebraic identities in 3-prime near-rings, Kragujev. J. Math., 42 No. 2 (2018) 247-256.
[6] A. Boua, Homoderivations and Jordan right ideals in 3-prime near-rings, AIP Conference Proceedings 2074, 020010 (2019).
[7] J. R. Clay, Near-rings: Geneses and Applications, Oxford Univ. Press, Oxford, 1992.
[8] M. M. El Sofy, Rings with some kinds of mappings, M.Sc. Thesis, Cairo University, Branch of Fayoum, 2000.
[9] A. Lakehal and A. Boua, Image encryption using the incidence matrix, Int. J. Appl. Math., 31 No. 2 (2018) 279-288.
[10] A. Melaibari, N. Muthana and A. Al-Kenani, Homoderivations on Rings, Gen. Math. Notes, 35 No. 1 (2016) 1{8.
[11] J. D. P. Meldrum, Near-rings and Their Links with Groups, Pitman, Marsh_eld, MA, 1985.
[12] G. Pilz, Near-rings, 2nd ed., 23, North Holland/American Elsevier, Amsterdam, 1983.
[13] X. K. Wang, Derivations in prime near-rings, Proc. Am. Math. Soc., 121 (1994) 361-366.