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

100%

Goldsmith B., Gong K.

Topological Algebra and its Applications

2015

tom 3

nr 1

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.

About the Algebraic Yuzvinski Formula

100%

Bruno A. G., Virili S.

Topological Algebra and its Applications

2015

tom 3

nr 1

The Algebraic Yuzvinski Formula expresses the algebraic entropy of an endomorphism of a finitedimensional rational vector space as the Mahler measure of its characteristic polynomial. In a recent paper, we have proved this formula, independently fromits counterpart – the Yuzvinski Formula – for the topological entropy proved by Yuzvinski in 1968. In this paper we first compare the proof of the Algebraic Yuzvinski Formula with a proof of the Yuzvinski Formula given by Lind and Ward in 1988, underlying the common ideas and the differences in the main steps. Then we describe several known applications of the Algebraic Yuzvinski Formula, and some related open problems are discussed. Finally,we give a new and purely algebraic proof of the Algebraic Yuzvinski Formula for the intrinsic algebraic entropy.

Ograniczanie wyników

2 Topological Algebra and its Applications

1 Bruno A. G.

1 Goldsmith B.

1 Gong K.

1 Virili S.

2 2015

Wyniki wyszukiwania

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

About the Algebraic Yuzvinski Formula