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Tytuł artykułu

When the intrinsic algebraic entropy is not really intrinsic

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The intrinsic algebraic entropy ent(ɸ) of an endomorphism ɸ of an Abelian group G can be computed using fully inert subgroups of ɸ-invariant sections of G, instead of the whole family of ɸ-inert subgroups. For a class of groups containing the groups of finite rank, aswell as those groupswhich are trajectories of finitely generated subgroups, it is proved that only fully inert subgroups of the group itself are needed to comput ent(ɸ). Examples show how the situation may be quite different outside of this class.
Wydawca
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2014-08-20
zaakceptowano
2015-08-16
online
2015-10-19
Twórcy
  • Dublin Institute of Technology, Aungier Street, Dublin 2, Ireland
autor
  • Dipartimento di Matematica, Universitá di Padova, Via Trieste 63, 35121 Padova, Italy, E-mail: salce@math.unipd.it
    Supported by "Progetti di Eccellenza 2011/12" of Fondazione CARIPARO
Bibliografia
  • [1] R. L. Adler, A. G. Konheim, M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309–319.
  • [2] S. Breaz, Finite torsion-free rank endomorphism ring, Carpathian J. Math. 31 (2015), no. 1, 39-43.
  • [3] U. Dardano, S. Rinauro, Inertial automorphisms of an Abelian group, Rend. Sem. Mat. Univ. Padova 127 (2012), 213–233.
  • [4] D. Dikranjan, A. Giordano Bruno, Topological entropy and algebraic entropy for group endomorphisms, Arhangelski˘ı A. V.,Moiz ud Din Khan; Kocinac L., ed., Proceedings Islamabad ICTA 2011, Cambridge Scientific Publishers 133–214.
  • [5] D. Dikranjan, A. Giordano Bruno, Entropy for Abelian groups, preprint arXiv:1007.0533.
  • [6] D.Dikranjan, A. Giordano Bruno, L. Salce, S. Virili, Intrinsic algebraic entropy, J. Pure Appl. Algebra 219 (2015), no. 7, 2933-2961.[WoS]
  • [7] D.Dikranjan, A. Giordano Bruno, L. Salce, S. Virili, Fully inert subgroups of divisible Abelian groups, J. Group Theory 16 (6)(2013), 915-939.[WoS]
  • [8] D. Dikranjan, B. Goldsmith, L. Salce, P. Zanardo, Algebraic entropy of endomorphisms of Abelian groups, Trans. Amer.Math.Soc. 361 (2009), 3401–3434.
  • [9] D. Dikranjan, L. Salce, P. Zanardo, Fully inert subgroups of free Abelian groups, Periodica Math. Hungarica 69 (2014), no. 1,69-78.[WoS][Crossref]
  • [10] P. Eklof, A. Mekler, Almost Free Modules. Set-Theoretic Methods, North-Holland, Amsterdam, 2002.
  • [11] L. Fuchs, Infinite Abelian Groups, Vol. I and II, Academic Press, 1970 and 1973.
  • [12] A. Giordano Bruno, S. Virili, The Algebraic Yuzvinski Formula, J. Algebra 423 (2015), 114-147.
  • [13] B. Goldsmith, K. Gong, A Note on Hopfian and co-Hopfian Abelian Groups, Contemporary Mathematics Vol. 576 (2012), 129–136.
  • [14] B. Goldsmith, P. Vámos, The Hopfian Exponent of an Abelian Group, Periodica Math. Hungarica 69 (2014), no. 1, 21-31.[WoS]
  • [15] B. Goldsmith, L. Salce, P. Zanardo, Fully inert submodules of torsion-free modules over the ring of p-adic integers,Colloquium Math. 136 (2014), no. 2, 169-178.[WoS]
  • [16] B. Goldsmith, L. Salce, P. Zanardo, Fully inert subgroups of Abelian p-groups, J. Algebra 419 (2014), 332-349.
  • [17] I. Kaplansky, Infinite Abelian Groups, (revised edition), The University of Michigan Press, 1969.
  • [18] J. Peters, Entropy on discrete Abelian groups, Adv. Math. 33 (1979), 1-13.
  • [19] L. Salce, P. Vámos, S. Virili Length functions, multiplicities and algebraic entropy, Forum Math. 25 (2013), no. 2, 255-282.
  • [20] S. A. Yuzvinski, Metric properties of endomorphisms of compact groups, Izv. Acad. Nauk SSSR, Ser. Mat. 29 (1965), 1295–1328 (in Russian). English Translation: Amer. Math. Soc. Transl. (2) 66 (1968), 63–98.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_taa-2015-0005
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