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Decomposing Gorenstein Rings as Connected Sums

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Extended Abstracts Spring 2015

Part of the book series: Trends in Mathematics ((RPCRMB,volume 5))

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Abstract

In 2012 Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings. They defined a connected sum of two Gorenstein local rings as an appropriate quotient of their fibre product. Given a Gorenstein ring, one would like to know whether it can be decomposed as a connected sum and if so, what are its components. We answer these questions in the case of a Gorenstein Artin local algebra over a field.

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References

  1. H. Ananthnarayan, Approximating Artinian rings by Gorenstein rings and three-standardness of the maximal ideal. Ph.D. Thesis, University of Kansas (2009)

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  2. H. Ananthnarayan, L.L. Avramov, W.F. Moore, Connected sums of Gorenstein local rings. J. Reine Angew. Math. 667, 149–176 (2012)

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  3. H. Ananthnarayan, E. Celikbas, Z. Yang, Decomposing Gorenstein rings as connected sums (Preprint)

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  4. W. Buczyńska, J. Buczyński, J. Kleppe, Z. Teitler, Apolarity and direct sum decomposability of polynomials. Preprint available at arXiv:1307.3314v2

  5. J. Elias, M.E. Rossi, Isomorphism classes of short Gorenstein local rings via Macaulay’s inverse system. Trans. Amer. Math. Soc. 364, 4589–4604 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Sally, Stretched Gorenstein rings. J. London Math. Soc. 20(2), 19–26 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  7. L. Smith, R.E. Stong, Projective bundle ideals and Poincaré duality algebras. J. Pure Appl. Algebra 215, 609–627 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, I.I.T. Bombay, Powai, 400076, Mumbai, India

    Hariharan Ananthnarayan

  2. Department of Mathematics, University of Connecticut, Storrs, CT, 06269, USA

    Ela Celikbas

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

    Zheng Yang

Authors
  1. Hariharan Ananthnarayan
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  2. Ela Celikbas
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  3. Zheng Yang
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Corresponding author

Correspondence to Hariharan Ananthnarayan .

Editor information

Editors and Affiliations

  1. Universitat Autònoma de Barcelona, Departament de Matemàtiques Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain

    Dolors Herbera

  2. Universitat Autònoma de Barcelona, Departament de Matemàtiques Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain

    Wolfgang Pitsch

  3. Universitat de Barcelona, Departament de MatemĂ tiques i InformĂ tica, Barcelona, Barcelona, Spain

    Santiago Zarzuela

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© 2016 Springer International Publishing Switzerland

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Ananthnarayan, H., Celikbas, E., Yang, Z. (2016). Decomposing Gorenstein Rings as Connected Sums. In: Herbera, D., Pitsch, W., Zarzuela, S. (eds) Extended Abstracts Spring 2015. Trends in Mathematics(), vol 5. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-45441-2_6

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