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On modules with chain condition on non-small submodules

Year 2023, Volume: 33 Issue: 33, 109 - 124, 09.01.2023

Avanish Kumar Chaturvedı Nirbhay Kumar

https://doi.org/10.24330/ieja.1195509

Abstract

In 1979, Fleury studied a class of modules with finite spanning dimension and dually a class of modules with ascending chain condition on non-small submodules was studied by Lomp and Ozcan in 2011. In the present work, we explore and investigate some new characterizations and properties of these classes of modules.

Keywords

ns-Noetherian module Noetherian module spanning dimension small submodule hollow module

References

  • D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56.
  • N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending Modules, Pitman Research Notes in Mathematics Series, Vol. 313, Longman Scientific and Technical, Harlow, 1994.
  • P. Fleury, A note on dualizing Goldie dimension, Canad. Math. Bull., 17(4) (1974), 511-517.
  • A. Ghorbani and A. Haghany, Generalized Hopfian modules, J. Algebra, 255(2) (2002), 324-341.
  • K. R. Goodearl and R. B. Warfield, An Introduction to Noncommutative Noetherian Rings, London Mathematical Society Student Texts, 2nd edn., Cambridge University Press, Cambridge, 2004.
  • W. Heinzer, C. Rotthaus and S. Wiegand, Examples of non-Noetherian domains inside power series rings, J. Commut. Algebra, 6(1) (2014), 53-93.
  • D. Keskin, On lifting modules, Comm. Algebra, 28(7) (2000), 3427-3440.
  • T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Vol. 131, 2nd edn., Springer-Verlag, New York, 2001.
  • C. Lomp and A. C. Ozcan, Fleury's spanning dimension and chain conditions on non-essential elements in modular lattices, Colloq. Math., 124(1) (2011), 133-144.
  • S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, London Mathematical Society, Lecture Note Series, Vol. 147, Cambridge University Press, Cambridge, 1990.
  • K. M. Rangaswamy, Modules with finite spanning dimension, Canad. Math. Bull., 20(2) (1977), 255-262.
  • P. F. Smith and M. R. Vedadi, Modules with chain conditions on non-essential submodules, Comm. Algebra, 32(5) (2004), 1881-1894.
  • R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, Philadelphia, PA, 1991.
  • O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, Graduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg-Berlin, 1975.

Year 2023, Volume: 33 Issue: 33, 109 - 124, 09.01.2023

Avanish Kumar Chaturvedı Nirbhay Kumar

https://doi.org/10.24330/ieja.1195509

Abstract

References

  • D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56.
  • N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending Modules, Pitman Research Notes in Mathematics Series, Vol. 313, Longman Scientific and Technical, Harlow, 1994.
  • P. Fleury, A note on dualizing Goldie dimension, Canad. Math. Bull., 17(4) (1974), 511-517.
  • A. Ghorbani and A. Haghany, Generalized Hopfian modules, J. Algebra, 255(2) (2002), 324-341.
  • K. R. Goodearl and R. B. Warfield, An Introduction to Noncommutative Noetherian Rings, London Mathematical Society Student Texts, 2nd edn., Cambridge University Press, Cambridge, 2004.
  • W. Heinzer, C. Rotthaus and S. Wiegand, Examples of non-Noetherian domains inside power series rings, J. Commut. Algebra, 6(1) (2014), 53-93.
  • D. Keskin, On lifting modules, Comm. Algebra, 28(7) (2000), 3427-3440.
  • T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Vol. 131, 2nd edn., Springer-Verlag, New York, 2001.
  • C. Lomp and A. C. Ozcan, Fleury's spanning dimension and chain conditions on non-essential elements in modular lattices, Colloq. Math., 124(1) (2011), 133-144.
  • S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, London Mathematical Society, Lecture Note Series, Vol. 147, Cambridge University Press, Cambridge, 1990.
  • K. M. Rangaswamy, Modules with finite spanning dimension, Canad. Math. Bull., 20(2) (1977), 255-262.
  • P. F. Smith and M. R. Vedadi, Modules with chain conditions on non-essential submodules, Comm. Algebra, 32(5) (2004), 1881-1894.
  • R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, Philadelphia, PA, 1991.
  • O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, Graduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg-Berlin, 1975.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Avanish Kumar Chaturvedı This is me

Nirbhay Kumar This is me

Publication Date January 9, 2023
Published in Issue Year 2023 Volume: 33 Issue: 33

Cite

APA Chaturvedı, A. K., & Kumar, N. (2023). On modules with chain condition on non-small submodules. International Electronic Journal of Algebra, 33(33), 109-124. https://doi.org/10.24330/ieja.1195509
AMA Chaturvedı AK, Kumar N. On modules with chain condition on non-small submodules. IEJA. January 2023;33(33):109-124. doi:10.24330/ieja.1195509
Chicago Chaturvedı, Avanish Kumar, and Nirbhay Kumar. “On Modules With Chain Condition on Non-Small Submodules”. International Electronic Journal of Algebra 33, no. 33 (January 2023): 109-24. https://doi.org/10.24330/ieja.1195509.
EndNote Chaturvedı AK, Kumar N (January 1, 2023) On modules with chain condition on non-small submodules. International Electronic Journal of Algebra 33 33 109–124.
IEEE A. K. Chaturvedı and N. Kumar, “On modules with chain condition on non-small submodules”, IEJA, vol. 33, no. 33, pp. 109–124, 2023, doi: 10.24330/ieja.1195509.
ISNAD Chaturvedı, Avanish Kumar - Kumar, Nirbhay. “On Modules With Chain Condition on Non-Small Submodules”. International Electronic Journal of Algebra 33/33 (January 2023), 109-124. https://doi.org/10.24330/ieja.1195509.
JAMA Chaturvedı AK, Kumar N. On modules with chain condition on non-small submodules. IEJA. 2023;33:109–124.
MLA Chaturvedı, Avanish Kumar and Nirbhay Kumar. “On Modules With Chain Condition on Non-Small Submodules”. International Electronic Journal of Algebra, vol. 33, no. 33, 2023, pp. 109-24, doi:10.24330/ieja.1195509.
Vancouver Chaturvedı AK, Kumar N. On modules with chain condition on non-small submodules. IEJA. 2023;33(33):109-24.