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Research Article

Some variants of ascending and descending chain conditions

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Pages 4324-4333 | Received 23 Mar 2020, Accepted 15 Apr 2021, Published online: 10 May 2021

References

  • Anderson, F. W., Fuller, K. R. (1974). Rings and categories of modules. In: Graduate Text in Math. Vol. 13. New York: Springer-Verlag Inc.
  • Aydoğdu, P., Özcan, A. Ç., Smith, P. F. (2011). Chain conditions on non summands. J. Algebra Appl. 10(03):475–489. DOI: 10.1142/S0219498811004707.
  • Chaturvedi, A. K. (2016). On Iso-retractable modules and rings. Presented at Proc. Algebra and Its Applications, ICAA Aligarh, India, 2014, Springer Proceedings in Mathematics and Statistics 174, Chapter 24, ISBN 981101650X, DOI: 10.1007/978-981-10-1651-6.24.
  • Chaturvedi, A. K. (2019). Iso-retractable modules and rings. Asian-Eur. J. Math. 12(01):1950013–1950020. DOI: 10.1142/S179355711950013X.
  • Chaturvedi, A. K., Prakash, S. (2022). Properties of modules and rings satisfying certain chain conditions. Southeast Asian Bull. Math. To appear.
  • Dastanpour, R., Ghorbani, A. (2017). Modules with epimorphisms on chain of submodules. J. Algebra Appl. 16(06):1750101–17501018. DOI: 10.1142/S0219498817501018.
  • Facchini, A., Nazemian, Z. (2016). Modules with chain conditions up to isomorphism. J. Algebra 453:578–601. DOI: 10.1016/j.jalgebra.2016.01.025.
  • Facchini, A., Nazemian, Z. (2017). Artinian dimension and isoradical of modules. J. Algebra 484:66–87. DOI: 10.1016/j.jalgebra.2017.03.039.
  • Facchini, A., Nazemian, Z. (2019). On iso-Noetherian and iso-Artinian modules. Contemp. Math. 730. DOI: 10.1090/conm/14707.
  • Goodearl, K. R., Warfield, R. B. (2004). An Introduction to Noncommutative Noetherian Rings, 2nd ed., London Mathematical Society Student Texts, Vol. 61. Cambridge: Cambridge University Press.
  • Lam, T. Y. (1998). Lectures on modules and rings. Graduate Texts in Mathematics, Vol. 139. New York, Berlin: Springer-Verlag.
  • Osofsky, B. L. (1992). Chain Conditions on essential submodules. Proc. Amer. Math. Soc. 114(1):11–19. DOI: 10.1090/S0002-9939-1992-1059630-4.
  • Pandeya, B. M., Chaturvedi, A. K., Gupta, A. J. (2012). Applications of epi-retractable modules. Bull. Iranian Math. Soc. 38(2):469–477.
  • Prakash, S., Chaturvedi, A. K. (2019). Iso-Noetherian rings and modules. Commun. Algebra 47(2):676–683. DOI: 10.1080/00927872.2018.1492591.
  • Smith, P. F. (2006). Compressible and related modules, In: Goeters, P., Jenda, O. M. G., eds., Abelian Groups, Rings, Modules and Homological Algebra. New York: Chapman & Hall/CRC, pp. 295–313.
  • Smith, P. F., Vedadi, M. R. (2004). Modules with chain conditions on non essential submodules. Commun. Algebra 32(5):1881–1894. DOI: 10.1081/AGB-120029910.
  • Tiwary, A. K., Pandeya, B. M. (1984). Modules whose nonzero endomorphisms are monomorphisms. Presented at Proc. Int. Symp. Algebra and Its Applications, New Delhi, 1981, In: Lect. Notes Pure Appl. Math., Vol. 91. New York: Marcel Dekker, Inc., pp. 199–203.

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