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A Construction of Totally Reflexive Modules

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Abstract

We construct infinite families of pairwise non-isomorphic indecomposable totally reflexive modules of high multiplicity. Under suitable conditions on the totally reflexive modules M and N, we find infinitely many non-isomorphic indecomposable modules arising as extensions of M by N. The construction uses the bimodule structure of \({Ext^{1}_{R}}((M,N)\) over the endomorphism rings of N and M. Our results compare with a recent theorem of Celikbas, Gheibi and Takahashi, and broaden the scope of that theorem.

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Authors and Affiliations

  1. Department of Mathematics Miami University, Oxford, OH, 45056, USA

    Hamid Rahmati

  2. Department of Mathematics Fairfield University, Fairfield, CT, 06824, USA

    Janet Striuli

  3. Department of Mathematics University of Nebraska, Lincoln, NE, 68588-0130, USA

    Roger Wiegand

Authors
  1. Hamid Rahmati
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  2. Janet Striuli
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  3. Roger Wiegand
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Corresponding author

Correspondence to Janet Striuli.

Additional information

Presented by Paul Smith.

This paper is dedicated to Alberto Facchini on the occasion of his sixtieth birthday

Roger Wiegand thanks the Simons Foundation for partial support for this research through the Simons Collaboration Grant number 209213.

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Rahmati, H., Striuli, J. & Wiegand, R. A Construction of Totally Reflexive Modules. Algebr Represent Theor 19, 103–111 (2016). https://doi.org/10.1007/s10468-015-9564-5

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  • DOI: https://doi.org/10.1007/s10468-015-9564-5

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