Skip to main content
SpringerLink
Log in
Book cover

Advances in Ring Theory pp 221–238Cite as

Birkhäuser

Weak Relative Injective M-Subgenerated Modules

  • Conference paper

  • 329 Accesses

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

Abstract

We study weak relative injective and relative tight modules in the category σ[M], where М is a right R-module. Many of the known results in the category of right R-modules are extended to σ[М]without assuming either М is projective or finitely generated. Conditions are given for a A-tight module to be weakly A-injective in σ[M]. Modules for which every submodule is weakly injective (tight) in σ[М] are characterized. Modules М for which every module in σ[М] is weakly injective and for which weakly injective modules are closed under direct sums are studied.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.H. Al-Huzali, S.K. Jain and S.R. López-Permouth, Rings whose cyclics have finite Goldie dimension, J. Algebra 153 (1992), 37–40.

    Article  MathSciNet  MATH  Google Scholar 

  2. A.H. Al-Huzali, S.K. Jain and S.R. López-Permouth, On the weak relative injectivity of rings and modules, Lecture notes in Math. 1448 (1990), 93–98.

    Article  Google Scholar 

  3. G.M.Brodskii, M.Saleh, Le Van Thuyet and R.Wisbauer, On weak injectivity of direct sum of modules,to be published.

    Google Scholar 

  4. V.P. Camillo, Modules whose quotients have finite Goldie dimension, Pacific J. Math., 69 (1977), 337–338.

    Article  MathSciNet  MATH  Google Scholar 

  5. N.V. Dung, D.V. Huynh, P.F. Smith and R. Wisbauer, “Extending modules”, Pitman Research Notes in Mathematics series, Longman, Harlow, 1994.

    Google Scholar 

  6. S.K. Jain and S.R. López-Permouth, A survey on theory of weakly injective modules, Computational Algebra, Lecture notes in Pure and applied Math.151, Dekker, New York (1994), 205–232

    Google Scholar 

  7. S.K. Jain and S.R. López-Permouth, Weakly injective modules over hereditary noetherian prime rings, J. Australian Math. Soc., (series A), 58 (1995), 287–297.

    Article  MATH  Google Scholar 

  8. S.K. Jain, S.R. López-Permouth and S. Singh, On a class of QI rings, Glasgow Math. J. 34 (1992), 75–81.

    Article  MathSciNet  MATH  Google Scholar 

  9. S.R. López-Permouth, Rings characterized by their weakly injective modules, Glasgow Math. J. 34 (1992), 349–353.

    Article  MathSciNet  MATH  Google Scholar 

  10. S.R. López-Permouth, S.Tariq Rizvi and M.F. Yousif, Some characterisations of semiprme Goldie rings, Glasgow Math. J. 35(1993), 357–365.

    Article  MathSciNet  MATH  Google Scholar 

  11. S.R. López-Permouth, and S.Tariq Rizvi, On certain classes of QI-rings, Methods in Module Theory (Colorado Springs C.O 1991), Lecture notes in pure and applied Math. 140, Dekker, New York, 1993, 227–235.

    Google Scholar 

  12. S.M. Mohamed and B.J. Müller, “Continuous and discrete modules”,London Math. Soc. Lecture Notes Series 147, Cambridge, 1990.

    Book  Google Scholar 

  13. N. Vanaja, All finitely generated M -subgenerated modules are extending, Comm. Algebra, 24(1996), 543–578.

    Article  MathSciNet  MATH  Google Scholar 

  14. R. Wisbauer, “Foundations of module and ring theory”, Gordon and Breach, Reading, 1991.

    Google Scholar 

  15. Y. Zhou, Weak injectivity and module classes, to be published.

    Google Scholar 

  16. Y. Zhou, Notes on weakly-semisimple rings, Bull. Austr. Math. Soc., 53(1996), 517–525.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hindu College, New Delhi, 110-007, India

    Saroj Malik

  2. Department of Mathematics, University of Mumbai, Mumbai, 400-098, India

    N. Vanaja

Authors
  1. Saroj Malik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Vanaja
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

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

    S. K. Jain

  2. Department of Mathematics, Ohio State University at Lima, Lima, OH, 45804, USA

    S. Tariq Rizvi

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this paper

Cite this paper

Malik, S., Vanaja, N. (1997). Weak Relative Injective M-Subgenerated Modules. In: Jain, S.K., Rizvi, S.T. (eds) Advances in Ring Theory. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1978-1_18

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1978-1_18

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7364-6

  • Online ISBN: 978-1-4612-1978-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation