Algebraic entropy for valuation domains

Paolo Zanardo

Topological Algebra and its Applications (2015)

  • Volume: 3, Issue: 1, page 34-44, electronic only
  • ISSN: 2299-3231

Abstract

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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].

How to cite

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Paolo Zanardo. "Algebraic entropy for valuation domains." Topological Algebra and its Applications 3.1 (2015): 34-44, electronic only. <http://eudml.org/doc/271758>.

@article{PaoloZanardo2015,
abstract = {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].},
author = {Paolo Zanardo},
journal = {Topological Algebra and its Applications},
keywords = {Algebraic entropy; valuation domains; algebraic entropy},
language = {eng},
number = {1},
pages = {34-44, electronic only},
title = {Algebraic entropy for valuation domains},
url = {http://eudml.org/doc/271758},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Paolo Zanardo
TI - Algebraic entropy for valuation domains
JO - Topological Algebra and its Applications
PY - 2015
VL - 3
IS - 1
SP - 34
EP - 44, electronic only
AB - 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].
LA - eng
KW - Algebraic entropy; valuation domains; algebraic entropy
UR - http://eudml.org/doc/271758
ER -

References

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  9. [9] L. Salce, P. Zanardo, Finitely generated modules over valuation rings, Comm. Algebra 12 (1984), no. 15-16, 1795–1812. [Crossref] Zbl0539.13007
  10. [10] L. Salce, P. Zanardo, A general notion of algebraic entropy and the rank-entropy, Forum Math. 21 (2009), no. 4, 561–587. [WoS] Zbl1203.20048
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  12. [12] P. Vámos, Additive functions and duality over Noetherian rings, Quart. J. Math. Oxford Ser. (2) 19 (1968) 43–55. [Crossref] Zbl0153.37101
  13. [13] S. Virili, Length functions of Grothendieck categories with applications to infinite group representations, arXiv: 1410.8306. 
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  15. [15] P. Zanardo, Multiplicative invariants and length functions over valuation domains, J. Commut. Algebra 3 (2011), no. 4, 561–587. [WoS][Crossref] Zbl1250.13016

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