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Algebraic entropy in locally linearly compact vector spaces. (English) Zbl 1391.37005
Fontana, Marco (ed.) et al., Rings, polynomials, and modules. Proceedings of the conferences “Recent advances in commutative ring and module theory”, Bressanone/Brixen, Italy, June 13–17, 2016 and “Conference on rings and polynomials”, Graz, Austria, July 3–8, 2016. Cham: Springer (ISBN 978-3-319-65872-8/hbk; 978-3-319-65874-2/ebook). 103-127 (2017).
Summary: We introduce algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as a natural extension of the algebraic entropy for endomorphisms of discrete vector spaces studied in [A. Giordano Bruno and L. Salce, Arab. J. Math. 1, No. 1, 69–87 (2012; Zbl 1282.15006)]. We show that the main properties continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem.
For the entire collection see [Zbl 1387.13003].

MSC:
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
15A03 Vector spaces, linear dependence, rank, lineability
15A04 Linear transformations, semilinear transformations
22B05 General properties and structure of LCA groups
20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
28D20 Entropy and other invariants
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