Algebraic entropy for valuation domains

• Autorzy: Paolo Zanardo
• Języki publikacji: EN

Abstrakty

EN

Let R be a non-discrete Archimedean valuation domain, G an R-module, Φ ∈ EndR(G).We compute the algebraic entropy entv(Φ), when Φ is restricted to a cyclic trajectory in G. We derive a special case of the Addition Theorem for entv, that is proved directly, without using the deep results and the difficult techniques of the paper by Salce and Virili [8].

Słowa kluczowe

EN

Algebraic entropy; valuation domains

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-05-28

zaakceptowano

2015-07-16

online

2015-09-14

Twórcy

autor

Paolo Zanardo

• Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova,
  Italy

Bibliografia

• [1] R. L. Adler, A. G. Konheim, M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309–319.
• [2] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401–414.
• [3] D. Dikranjan, A. Giordano Bruno, Discrete dynamical systems in group theory, Note Mat. 33 (2013), no. 1, 1–48.
• [4] D. Dikranjan, B. Goldsmith, L. Salce, P. Zanardo, Algebraic entropy for abelian groups, Trans. Amer.Math. Soc. 361 (2009), no. 7, 3401–3434.
• [5] L. Fuchs, L. Salce, Modules over non-Noetherian domains, Mathematical Surveys and Monographs, 84. American Mathematical Society, Providence, RI, 2001.
• [6] D.G. Northcott, M. Reufel, A generalization of the concept of length, Quart. J. Math. Oxford (2) 16 (1965) 297–321.
• [7] L. Salce, P. Vámos, S. Virili, Length functions, multiplicities and algebraic entropy, ForumMath. 25 (2013), no. 2, 255–282.
• [8] L. Salce, S. Virili, The addition theorem for algebraic entropies induced by non-discrete length functions, to appear.
• [9] L. Salce, P. Zanardo, Finitely generated modules over valuation rings, Comm. Algebra 12 (1984), no. 15-16, 1795–1812. [Crossref]
• [10] L. Salce, P. Zanardo, A general notion of algebraic entropy and the rank-entropy, Forum Math. 21 (2009), no. 4, 561–587. [WoS]
• [11] P. Vámos, Length functions on modules, Ph.D. thesis, University of Shefleld, 1968.
• [12] P. Vámos, Additive functions and duality over Noetherian rings, Quart. J. Math. Oxford Ser. (2) 19 (1968) 43–55. [Crossref]
• [13] S. Virili, Length functions of Grothendieck categories with applications to infinite group representations, arXiv: 1410.8306.
• [14] M. D. Weiss, Algebraic and other entropies of group endomorphisms,Math. Systems Theory, 8 (1974/75), no. 3, 243–248.
• [15] P. Zanardo, Multiplicative invariants and length functions over valuation domains, J. Commut. Algebra 3 (2011), no. 4, 561–587. [WoS][Crossref]

Identyfikatory

DOI

10.1515/taa-2015-0004