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On modules with chain condition on non-small submodules

Yıl 2023, Cilt: 33 Sayı: 33, 109 - 124, 09.01.2023
https://doi.org/10.24330/ieja.1195509

Öz

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.

Kaynakça

  • 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.
Yıl 2023, Cilt: 33 Sayı: 33, 109 - 124, 09.01.2023
https://doi.org/10.24330/ieja.1195509

Öz

Kaynakça

  • 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.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Avanish Kumar Chaturvedı Bu kişi benim

Nirbhay Kumar Bu kişi benim

Yayımlanma Tarihi 9 Ocak 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 33 Sayı: 33

Kaynak Göster

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. Ocak 2023;33(33):109-124. doi:10.24330/ieja.1195509
Chicago Chaturvedı, Avanish Kumar, ve Nirbhay Kumar. “On Modules With Chain Condition on Non-Small Submodules”. International Electronic Journal of Algebra 33, sy. 33 (Ocak 2023): 109-24. https://doi.org/10.24330/ieja.1195509.
EndNote Chaturvedı AK, Kumar N (01 Ocak 2023) On modules with chain condition on non-small submodules. International Electronic Journal of Algebra 33 33 109–124.
IEEE A. K. Chaturvedı ve N. Kumar, “On modules with chain condition on non-small submodules”, IEJA, c. 33, sy. 33, ss. 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 (Ocak 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 ve Nirbhay Kumar. “On Modules With Chain Condition on Non-Small Submodules”. International Electronic Journal of Algebra, c. 33, sy. 33, 2023, ss. 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.