ON 3-ADDITIVE MAPPINGS AND COMMUTATIVITY IN CERTAIN RINGS

- Journal title : Communications of the Korean Mathematical Society
- Volume 22, Issue 1, 2007, pp.41-51
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2007.22.1.041

Title & Authors

ON 3-ADDITIVE MAPPINGS AND COMMUTATIVITY IN CERTAIN RINGS

Park, Kyoo-Hong; Jung, Yong-Soo;

Park, Kyoo-Hong; Jung, Yong-Soo;

Abstract

Let R be a ring with left identity e and suitably-restricted additive torsion, and Z(R) its center. Let H : be a symmetric 3-additive mapping, and let h be the trace of H. In this paper we show that (i) if for each , $$n=<<\cdots,\;x>,\;\cdots,x>{\in}Z(R)$$ with fixed, then h is commuting on R. Moreover, h is of the form , where , is an additive commuting mapping, is the commuting trace of a bi-additive mapping and the mapping is the trace of a symmetric 3-additive mapping; (ii) for each , either $n=0\;or\;<n,\;x^m>=0$ with fixed, then h = 0 on R, where denotes the product yx+xy and Z(R) is the center of R. We also present the conditions which implies commutativity in rings with identity as motivated by the above result.

Keywords

skew-commuting mappings;skew-centralizing mappings;commuting mappings;derivations;

Language

English

Cited by

References

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