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Essential Extensions of a Direct Sum of Simple Modules-II

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Modules and Comodules

Part of the book series: Trends in Mathematics ((TM))

Abstract

It is shown that a semi-regular ring R with the property that each essential extension of a direct sum of simple right R-modules is a direct sum of quasi-injective right R-modules is right noetherian.

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References

  1. K.I. Beidar and S.K. Jain, When Is Every Module with Essential Socle a Direct Sums of Quasi-Injectives?, Communications in Algebra, 33,11 (2005), 4251–4258.

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  2. K.I. Beidar, S.K. Jain and Ashish K. Srivastava, Essential Extensions of a Direct Sum of Simple Modules, Groups, Rings and Algebras, Contemporary Mathematics, AMS, 420 (2006), 15–23.

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  3. K.R. Goodearl, von Neumann Regular Rings, Krieger Publishing Company, Malabar, Florida, 1991.

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  4. S.K. Jain, S.H. Mohamed, Surjeet Singh, Rings In Which Every Right Ideal Is Quasi-Injective, Pacific Journal of Mathematics, Vol. 31, No. 1 (1969), 73–79.

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  5. S.H. Mohamed and B.J. Muller, Continuous and Discrete Modules, Cambridge University Press, 1990.

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  6. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, 1991.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ohio University, Athens, Ohio, 45701, USA

    S. K. Jain

  2. Department of Mathematics & Computer Science, St. Louis University, St. Louis, MO, 63103, USA

    Ashish K. Srivastava (Assistant Professor)

Authors
  1. S. K. Jain
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  2. Ashish K. Srivastava
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, UK

    Tomasz Brzeziński

  2. Departamento de Alxebra, Universidade de Santiago, 15782, Santiago de Compostela, Spain

    José Luis Gómez Pardo

  3. Instituto de Matemática e Estatística da, Universidade de São Paulo (IME-USP), Rua do Matão, 1010 Cidade Universitária, CEP 05508-090, São Paulo - SP, Brasil

    Ivan Shestakov

  4. Department of Mathematics, University of Glasgow, University Gardens, Glasgow, G12 8QW, Scotland,UK

    Patrick F. Smith

Additional information

Dedicated to Robert Wisbauer on his 65th Birthday

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Jain, S.K., Srivastava, A.K. (2008). Essential Extensions of a Direct Sum of Simple Modules-II. In: Brzeziński, T., Gómez Pardo, J.L., Shestakov, I., Smith, P.F. (eds) Modules and Comodules. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8742-6_15

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