On dependent elements in rings

Joso Vukman and Irena Kosi-Ulbl

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-12

Abstract:

Let R be an associative ring. An element a ∈ R is said to be dependent on a mapping F : R → R in case F ( x ) a = a x holds for all x ∈ R . In this paper, elements dependent on certain mappings on prime and semiprime rings are investigated. We prove, for example, that in case we have a semiprime ring R , there are no nonzero elements which are dependent on the mapping α + β , where α and β are automorphisms of R .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:548684

DOI: 10.1155/S0161171204311221

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