Abstract
In this chapter we will study d-free sets and some related (but more complicated) concepts such as (t; d)-freeness and (*; t; d)-freeness. Besides introducing these concepts and considering their formal properties, our main objective will be to present various constructions that yield new d-free (resp. (t; d)-free) sets from given ones. In Chapter 5 we shall actually establish d-freeness of certain particular classes of sets and then use the results of the present chapter to show that the list of d-free sets is really quite extensive.
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Literature and Comments
K. I. Beidar, M. Brešar, M.A. Chebotar, W. S. Martindale 3rd, On functional identities in prime rings with involution II, Comm. Algebra 28 (2000), 3169–3183.
K. I. Beidar, M. Brešar, M.A. Chebotar, W. S. Martindale 3rd, On Herstein’s Lie map conjectures, II, J. Algebra 238 (2001), 239–264.
K. I. Beidar, M.A. Chebotar, On functional identities and d-free subsets of rings I, Comm. Algebra 28 (2000), 3925–3951.
K. I. Beidar, W. S. Martindale 3rd, On functional identities in prime rings with involution, J. Algebra 203 (1998), 491–532.
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© 2007 Birkhäuser Verlag
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(2007). Constructing d-Free Sets. In: Functional Identities. Frontiers in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7796-0_3
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DOI: https://doi.org/10.1007/978-3-7643-7796-0_3
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7795-3
Online ISBN: 978-3-7643-7796-0
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