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Semigroup ideals with multiplicative semiderivations and commutativity of 3-prime near-rings


Abstract


In the present paper, we introduce the notion of multiplicative semiderivation and prove some theorems in the setting of a semigroup ideal of a 3-prime near-ring admitting a multiplicative semiderivation. Thereby, it is shown that under appropriate additional hypotheses a near-ring must be a commutative ring. Furthermore, an example is given to illustrate that the 3-primeness hypothesis is not superfluous.

DOI Code: 10.1285/i15900932v42n2p43

Keywords: prime near-rings; multiplicative derivations; commutativity

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