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We prove some theorems showing that a right Jordan ideal or a left Jordan ideal of a $3$-prime near-ring must be commutative if it admits a nonzero derivation acting as a homomorphism or an antihomomorphism. Moreover, we give examples proving necessity of the conditions given.\bigskip
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참고문헌 (9)
참고문헌 신청
M. Ashraf / 2000 / On $({\sigma},\;{\tau})$ -derivations in certain classes of rings / Rad. Mat. 9(2):187~192
A. Asma / 2003 / On Lie ideals with derivations as homomorphisms and anti-homomorphisms / Acta Math. Hungar. 101(1-2):79~82
H. E. Bell / 1989 / Rings in which derivations satisfy certain algebraic conditions / Acta Math. Hungar. 53(3-4):339~346
H. E. Bell / 1985 / On derivations in near-rings, in Near-rings and near-fields (Tubingen, 1985) / North-Holland Math. Stud. 137:31~35
A. Boua / 2018 / Commutativity of near-rings with certain constrains on Jordan ideals / Bol. Soc. Paran. Mat. 36(4):159~170
A. Asma / 2003 / On Lie ideals with derivations as homomorphisms and anti-homomorphisms / Acta Math. Hungar. 101(1-2):79~82
H. E. Bell / 1989 / Rings in which derivations satisfy certain algebraic conditions / Acta Math. Hungar. 53(3-4):339~346
H. E. Bell / 1985 / On derivations in near-rings, in Near-rings and near-fields (Tubingen, 1985) / North-Holland Math. Stud. 137:31~35
A. Boua / 2018 / Commutativity of near-rings with certain constrains on Jordan ideals / Bol. Soc. Paran. Mat. 36(4):159~170
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