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Essential Extensions of a Direct Sum of Simple Modules-II

  • S. K. Jain
  • Ashish K. Srivastava
Conference paper
Part of the Trends in Mathematics book series (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.

Keywords

Right noetherian essential extension quasi-injective module simple module von Neumann regular ring 

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References

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    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.zbMATHCrossRefMathSciNetGoogle Scholar
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    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.MathSciNetGoogle Scholar
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    K.R. Goodearl, von Neumann Regular Rings, Krieger Publishing Company, Malabar, Florida, 1991.zbMATHGoogle Scholar
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    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.zbMATHMathSciNetGoogle Scholar
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    S.H. Mohamed and B.J. Muller, Continuous and Discrete Modules, Cambridge University Press, 1990.Google Scholar
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    R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, 1991.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • S. K. Jain
    • 1
  • Ashish K. Srivastava
    • 2
  1. 1.Department of MathematicsOhio UniversityAthensUSA
  2. 2.Department of Mathematics & Computer ScienceSt. Louis UniversitySt. LouisUSA

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