On NCS modules and rings

Abstract We give some conditions as to when a (finite) direct sum of NCS modules (if no non-zero complement submodule is small) is again NCS, and also provide various conditions to be sufficient for a submodule of an NCS module to be NCS. Some comparisons between QF-rings, GP-injective rings, AGP-rings and NCS rings are investigated.

[1]  T. C. Quynh,et al.  On Automorphism-Invariant Rings with Chain Conditions , 2020, Vietnam Journal of Mathematics.

[2]  T. C. Quynh,et al.  Essentially ADS modules and rings , 2019, Contemporary Mathematics.

[3]  T. C. Quynh,et al.  On dual automorphism-invariant and superfluous ADS-modules , 2019, Contemporary Mathematics.

[4]  Wenxi Li,et al.  Generalization of CS condition , 2017 .

[5]  T. C. Quynh,et al.  On ADS Modules and Rings , 2014 .

[6]  Adel Alahmadi,et al.  ADS modules , 2012, 1207.1959.

[7]  T. C. Quynh,et al.  On General Injective Rings with Chain Conditions , 2009 .

[8]  Jianlong Chen,et al.  On Artiness of Right CF Rings , 2004 .

[9]  Jianlong Chen,et al.  On general principally injective rings , 1999 .

[10]  W. K. Nicholson,et al.  Annihilators and the CS-condition , 1998, Glasgow Mathematical Journal.

[11]  D. Huynh,et al.  A note on quasi-Frobenius rings , 1996 .

[12]  W. K. Nicholson,et al.  Principally Injective Rings , 1995 .

[13]  Frank W. Anderson,et al.  Rings and Categories of Modules , 1974 .

[14]  J. Björk.  Rings satisfying certain chain conditions. , 1970 .