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Commutativity of Jordan ideals in 3-prime near-rings with derivations

Abdelkarim Boua
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회논문집 (Communications of the KMS)|제33권 제1호|pp. 37-44

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키워드

derivationscommutativity$3$-prime near-ringsJordan ideal
주제분류수학

초록

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

Abstract

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

참고문헌 (9)

  1. M. Ashraf, "On <TEX>$({\sigma},\;{\tau})$<", TEX>-derivations in certain classes of rings, 2000, pp.9(2), 187~192
  2. A. Asma, "On Lie ideals with derivations as homomorphisms and anti-homomorphisms", Acta Math. Hungar., 101(1-2), pp.79~82 (2003)[DOI]
  3. H. E. Bell, "Rings in which derivations satisfy certain algebraic conditions", Acta Math. Hungar., 53(3-4), pp.339~346 (1989)[DOI]
  4. H. E. Bell, "On derivations in near-rings, in Near-rings and near-fields (Tubingen, 1985)", North-Holland Math. Stud., 137, pp.31~35 (1985)
  5. A. Boua, "Commutativity of near-rings with certain constrains on Jordan ideals", Bol. Soc. Paran. Mat., 36(4), pp.159~170 (2018)[DOI]
  6. A. A. M. Kamal, "Existence of derivations on near-rings", Math. Slovaca, 63(3), pp.431~448 (2013)
  7. G. Pilz, "Near-rings, second edition", North-Holland Mathematics Studies, 23 (1983)
  8. X. K. Wang, "Derivations in prime near-rings", Proc. Amer. Math. Soc., 121(2), pp.361~366 (1994)[DOI]
  9. M. Yenig, "On prime and semiprime rings with <TEX>${\alpha}$<", TEX>-derivations, 1994, pp.18(3), 280~283

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