Some characterizations of small projective modules
PDF (Vietnamese)

How to Cite

Hà NTT. Some characterizations of small projective modules. hueuni-jns [Internet]. 2020Jun.30 [cited 2024May18];129(1C):117-23. Available from:


The aim of this paper is to introduce a generalization of projective modules, that is small projective modules. We give some new results on this kind of module and obtain some characterizations of some related rings. Then, we show the relationship between small projective modules and automorphism-coinvariant modules. The results in the article was introduced in [1]. Here, we add examples and clearly demonstrate the prove of some unproven results in the above article.
PDF (Vietnamese)


  1. Quynh TC, Abyzov ATT, Yildirim T. Modules close to the automorphism-invariant and coinvariant. J Algebra and its Appl. 2019;18(12):1950235.
  2. Anderson FW, Fuller KR. Rings and Categories of Modules. New York: Springer-Verlag; 1974.
  3. Dung NV, Huynh DV, Smith PF, Wisbauer R. Extending modules. Pitman Research Notes in Math. New York: Longman. Harlow; 1994.
  4. Asensio PA, Tütüncü DK, Srivastava AK. Modules invariant under automorphisms of their covers and envelopes. Israel J Math. 2015;206:457-482.
  5. Mohammed SH, Müller J. Continous and Discrete Modules. Cambridge: Cambridge Univ Press; 1990. 126 p.
  6. Nicholson WK, Yousif MF. Quasi-Frobenius Rings. Cambridge: Cambridge Univ Press; 2003. Background; p. 1-35.
  7. Wisbauer R. Foundations of Module and Ring Theory. Düsseldorf: Gordon and Breach, Reading; 1991.
  8. Clark J, Lomp C, Vanaja N, Wisbauer R. Lifting Modules: Supplements and projectivity in module theory. Basel: Birkhauser Verlag; 2006.
  9. Singh S, Srivastava AK. Dual automorphism-invariant modules. J Algebra. 2012;371:262-275.
  10. Crawley P, Jonnson B. Refinements for infinite direct decompositions of algebraic systems. Pacific J Math. 1964;14 (3):755-1127.
  11. Abyzov AN. Almost Projective and Almost Injective Modules. Mathematical Notes. 2018;103:3-17.
Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Copyright (c) 2020 Array