Abstract
In Section 2.1 we will introduce the concept of the strong degree of a unital ring. The definition involves a condition which is rather technical, but we shall see that the strong degree can be rather easily computed for certain classes of rings. The main reason for dealing with this concept is its connection with functional identities - this will be the topic of Section 2.4. Before that, in Sections 2.2 and 2.3, we will consider certain versions of the concept of d-freeness (called strong d-freeness and strong (t; d)-freeness). Unlike in Chapter 1, we shall now consider these notions in a rigorous manner.
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Literature and Comments
J. Alaminos, M. Brešar, A. R. Villena, The strong degree and the structure of Lie and Jordan derivations from von Neumann algebras, Math. Proc. Camb. Phil. Soc. 137 (2004), 441–463.
K. I. Beidar, M. Brešar, M.A. Chebotar, Functional identities revised: the fractional and the strong degree, Comm. Algebra 30 (2002), 935–969.
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). The Strong Degree and the FI-Degree. In: Functional Identities. Frontiers in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7796-0_2
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DOI: https://doi.org/10.1007/978-3-7643-7796-0_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7795-3
Online ISBN: 978-3-7643-7796-0
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