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On the ring of inertial endomorphisms of an abelian group

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Abstract

An endomorphisms \({\varphi }\) of an abelian group \(A\) is said inertial if each subgroup \(H\) of \(A\) has finite index in \(H+\varphi (H)\). We study the ring of inertial endomorphisms of an abelian group. We obtain a satisfactory description modulo the ideal of finitary endomorphisms. Also the corresponding problem for vector spaces is considered.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni “R.Caccioppoli”, Università di Napoli “Federico II”, Via Cintia, Monte S. Angelo, 80126, Naples, Italy

    Ulderico Dardano

  2. Dipartimento di Matematica, Informatica ed Economia, Università della Basilicata, Via dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Silvana Rinauro

Authors
  1. Ulderico Dardano
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  2. Silvana Rinauro
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Correspondence to Ulderico Dardano.

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Communicated by Salvatore Rionero.

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Dardano, U., Rinauro, S. On the ring of inertial endomorphisms of an abelian group. Ricerche mat. 63 (Suppl 1), 103–115 (2014). https://doi.org/10.1007/s11587-014-0199-3

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  • DOI: https://doi.org/10.1007/s11587-014-0199-3

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