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

Brendan Goldsmith; Ketao Gong

Topological Algebra and its Applications (2015)

  • Volume: 3, Issue: 1
  • ISSN: 2299-3231

Abstract

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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.

How to cite

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Brendan Goldsmith, and Ketao Gong. "Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups." Topological Algebra and its Applications 3.1 (2015): null. <http://eudml.org/doc/276012>.

@article{BrendanGoldsmith2015,
abstract = {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.},
author = {Brendan Goldsmith, Ketao Gong},
journal = {Topological Algebra and its Applications},
keywords = {algebraic entropy; adjoint entropy; direct sums; matrix of endomorphisms; Abelian groups},
language = {eng},
number = {1},
pages = {null},
title = {Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups},
url = {http://eudml.org/doc/276012},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Brendan Goldsmith
AU - Ketao Gong
TI - Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups
JO - Topological Algebra and its Applications
PY - 2015
VL - 3
IS - 1
SP - null
AB - 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.
LA - eng
KW - algebraic entropy; adjoint entropy; direct sums; matrix of endomorphisms; Abelian groups
UR - http://eudml.org/doc/276012
ER -

References

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