TY - JOUR T1 - On modules with chain condition on non-small submodules AU - Chaturvedı, Avanish Kumar AU - Kumar, Nirbhay PY - 2023 DA - January DO - 10.24330/ieja.1195509 JF - International Electronic Journal of Algebra JO - IEJA PB - Abdullah HARMANCI WT - DergiPark SN - 1306-6048 SP - 109 EP - 124 VL - 33 IS - 33 LA - en AB - 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. KW - ns-Noetherian module KW - Noetherian module KW - spanning dimension KW - small submodule KW - hollow module CR - D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56. CR - 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. CR - P. Fleury, A note on dualizing Goldie dimension, Canad. Math. Bull., 17(4) (1974), 511-517. CR - A. Ghorbani and A. Haghany, Generalized Hopfian modules, J. Algebra, 255(2) (2002), 324-341. CR - 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. CR - W. Heinzer, C. Rotthaus and S. Wiegand, Examples of non-Noetherian domains inside power series rings, J. Commut. Algebra, 6(1) (2014), 53-93. CR - D. Keskin, On lifting modules, Comm. Algebra, 28(7) (2000), 3427-3440. CR - T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Vol. 131, 2nd edn., Springer-Verlag, New York, 2001. CR - 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. CR - S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, London Mathematical Society, Lecture Note Series, Vol. 147, Cambridge University Press, Cambridge, 1990. CR - K. M. Rangaswamy, Modules with finite spanning dimension, Canad. Math. Bull., 20(2) (1977), 255-262. CR - P. F. Smith and M. R. Vedadi, Modules with chain conditions on non-essential submodules, Comm. Algebra, 32(5) (2004), 1881-1894. CR - R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, Philadelphia, PA, 1991. CR - O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, Graduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg-Berlin, 1975. UR - https://doi.org/10.24330/ieja.1195509 L1 - https://dergipark.org.tr/en/download/article-file/2734789 ER -