On Adjoint Entropy of Abelian Groups

Brendan Goldsmith

doi:10.21427/rr3e-yg14

On Adjoint Entropy of Abelian Groups

Brendan Goldsmith

Technological University Dublin

Research output: Contribution to journal › Article › peer-review

Abstract

The theory of endomorphism rings of algebraic structures allows, in a natural way, a systematic approach based on the notion of entropy borrowed from dynamical systems. In the present work we introduce a \lq dual\rq \ notion based upon the replacement of the finite groups used in the definition of algebraic entropy, by subgroups of finite index. The basic properties of this new entropy are established and a connection to Hopfian groups is investigated.

Original language	English
Journal	Communications in Algebra
DOIs	https://doi.org/10.21427/rr3e-yg14
Publication status	Published - 1 Jan 2011

Keywords

endomorphism rings
algebraic structures
entropy
dynamical systems
finite groups
algebraic entropy
subgroups of finite index
Hopfian groups

Access to Document

10.21427/rr3e-yg14Licence: CC BY-NC-SA

Cite this

@article{7136c607f4974ae6bdb293d4c471aba1,

title = "On Adjoint Entropy of Abelian Groups",

abstract = "The theory of endomorphism rings of algebraic structures allows, in a natural way, a systematic approach based on the notion of entropy borrowed from dynamical systems. In the present work we introduce a \lq dual\rq \ notion based upon the replacement of the finite groups used in the definition of algebraic entropy, by subgroups of finite index. The basic properties of this new entropy are established and a connection to Hopfian groups is investigated.",

keywords = "endomorphism rings, algebraic structures, entropy, dynamical systems, finite groups, algebraic entropy, subgroups of finite index, Hopfian groups",

author = "Brendan Goldsmith",

year = "2011",

month = jan,

day = "1",

doi = "10.21427/rr3e-yg14",

language = "English",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

}

TY - JOUR

T1 - On Adjoint Entropy of Abelian Groups

AU - Goldsmith, Brendan

PY - 2011/1/1

Y1 - 2011/1/1

N2 - The theory of endomorphism rings of algebraic structures allows, in a natural way, a systematic approach based on the notion of entropy borrowed from dynamical systems. In the present work we introduce a \lq dual\rq \ notion based upon the replacement of the finite groups used in the definition of algebraic entropy, by subgroups of finite index. The basic properties of this new entropy are established and a connection to Hopfian groups is investigated.

AB - The theory of endomorphism rings of algebraic structures allows, in a natural way, a systematic approach based on the notion of entropy borrowed from dynamical systems. In the present work we introduce a \lq dual\rq \ notion based upon the replacement of the finite groups used in the definition of algebraic entropy, by subgroups of finite index. The basic properties of this new entropy are established and a connection to Hopfian groups is investigated.

KW - endomorphism rings

KW - algebraic structures

KW - entropy

KW - dynamical systems

KW - finite groups

KW - algebraic entropy

KW - subgroups of finite index

KW - Hopfian groups

U2 - 10.21427/rr3e-yg14

DO - 10.21427/rr3e-yg14

M3 - Article

SN - 0092-7872

JO - Communications in Algebra

JF - Communications in Algebra

ER -

On Adjoint Entropy of Abelian Groups

Abstract

Keywords

Access to Document

Fingerprint

Cite this