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Tytuł artykułu

Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Necessary and sufficient conditions to ensure that the direct sum of two Abelian groups with zero entropy is again of zero entropy are still unknown; interestingly the same problem is also unresolved for direct sums of Hopfian and co-Hopfian groups.We obtain sufficient conditions in some situations by placing restrictions on the homomorphisms between the groups. There are clear similarities between the various cases but there is not a simple duality involved.
Wydawca
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-08-07
zaakceptowano
2015-08-13
online
2015-11-09
Twórcy
  • School of Mathematical Sciences, Dublin Institute of Technology, Aungier Street, Dublin 8, Ireland
autor
  • School of Mathematics and Statistics, Hubei Engineering University, No. 272, Jiaotong
    Road, Xiaogan City, Hubei Province, 432000, P.R.China
Bibliografia
  • [1] R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological Entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319.
  • [2] R. Baer, Groups without proper isomorphic quotient groups, Bull. Amer. Math. Soc. 50 (1944), 267-278.
  • [3] G. Baumslag, Hopficity and Abelian Groups, in Topics in Abelian Groups (Proc. Sympos., New Mexico State Univ.), ScottForesman and Co., Chicago, 1963. pp.331-335.
  • [4] A. L. S. Corner, Three examples on hopficity in torsion-free abelian groups, Acta Math. Hungarica 16, No. 3-4(1965), 303-310.[Crossref]
  • [5] A. L. S. Corner, On Endomorphism Rings of Primary Abelian Groups, Quart. J. Math. Oxford.(2) 20, (1969), 277-296.[Crossref]
  • [6] D. Dikranjan, A. Giordano Bruno and L. Salce, Adjoint Algebraic Entropy, J. Algebra 324(2010), 442-463.[WoS]
  • [7] D. Dikranjan, B. Goldsmith, L. Salce and P. Zanardo, Algebraic Entropy for Abelian Groups, Tran. Amer. Math. Soc. 361, No.7(2009), 3401-3434.
  • [8] L. Fuchs, Infinite Abelian Groups, Vol I, II, Academic Press, 1970 and 1973.
  • [9] B. Goldsmith, K. Gong, On Adjoint Entropy of Abelian Groups, Comm. Algebra 40, No. 3(2012), 972-987.[Crossref]
  • [10] Goldsmith and K. Gong, A note on Hopfian and co-Hopfian Abelian groups, Contemporary Maths. Vol. 576, 2012. Serieseditors: M. Droste, L. Fuchs, L. Strügmann, K. Tent and M. Ziegler.
  • [11] B. Goldsmith and P. Vámos, The Hopfian Exponent of an Abelian Group, to appear in the special volume of Periodica Math.Hungarica dedicated to László Fuchs.
  • [12] K. Gong, Entropy in Abelian Groups, Doctoral Thesis, School ofMathematical Sciences, Dublin Institute of Technology, 2012.
  • [13] P. Griflth, Purely indecomposable torsion-free groups, Proc. Amer. Math. Soc. 18(1967), 738-742.
  • [14] R. Hirshon, Some Theorems On Hopficity, Tran. Amer. Math. Soc. 141(1969), 229-244.
  • [15] Y. Li, On the cohopficity of the direct product of cohopfian groups, Comm. Algebra 35, (2007), 3226-3235.[Crossref]
  • [16] J. Peters, Entropy on Discrete Abelian Groups, Adv. Math. 33(1979), 1-13.
  • [17] R. S. Pierce, Homomorphisms of primary Abelian groups, in Topics in Abelian Groups, Scott Foresman (1963) 215 - 310.
  • [18] L. Salce, P. Vámos, S. Virili, Length functions, multiplicities and algebraic entropy, Forum Math. 25, No. 2(2013), 255-282.[WoS]
  • [19] L. Salce and P. Zanardo, Abelian groups of zero adjoint entropy Colloq. Math. 121, (2010), 45-62.[WoS]
  • [20] W. Vasconcelos, Injective Endomorphisms of Finitely Generated Modules, Proc. Amer. Math. Soc. 25, (1970), 900-901.
  • [21] M. D. Weiss, Algebraic and Other Entropies of Group Endomorphisms, Math. Systems. Theory. Vol. 8, No. 3. 243-248.[Crossref]
  • [22] P. Zanardo, Multiplicative invariants and length functions over valuation domains, J. Commut. Algebra. Vol 3, No. 4 (2011),561-587.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_taa-2015-0007
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