Automorphism invariant modules on the right Goldie ring
Vol. 131 No. 1A (2022), Original Article
Vol. 131 No. 1A (2022)

Automorphism invariant modules on the right Goldie ring

Original Article
https://doi.org/10.26459/hueunijns.v131i1A.6418
Published 2022-03-31
Le Van Thuyet
University of Education, Hue University, 34 Le Loi St., Hue, Vietnam
Dao Thi Trang*
University of Education, Hue University, 34 Le Loi St., Hue, Vietnam
Truong Cong Quynh
The University of Danang - University of Science and Education, 45 Ton Duc Thang St., Da Nang, Vietnam
PDF (Vietnamese)

Keywords

automorphism invariant modules
right Goldie ring
nonsingular Môđun nội xạ
môđun bất biến đẳng cấu
vành Goldie phải
môđun không suy biến
vành tổng quát hóa của chuỗi tổng quát

How to Cite

1.
Lê VT, Trang Đào T, Trương CQ. Automorphism invariant modules on the right Goldie ring. hueuni-jns [Internet]. 2022Mar.31 [cited 2024Nov.14];131(1A):95-100. Available from: http://222.255.146.83/index.php/hujos-ns/article/view/6418
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Abstract

In this paper, we study some properties of automorphism invariant modules on the right Goldie ring and state some properties related to this class of modules. In addition, we confirmed some problems related to the nonsingular automorphism invariant ring.

https://doi.org/10.26459/hueunijns.v131i1A.6418
PDF (Vietnamese)

References

  1. Johnson RE, Wong ET. Quasi-injective modules and irreducible rings. J Lond Math Soc. 1961;(36):260-268.
  2. Lee TK, Zhou Y. Modules which are invariant under automorphisms of their injective hulls. J Algebra Appl. 2013;12(2).
  3. Lam TY. Lectures on Modules and Rings. Berlin: Springer. 1998.
  4. Jain SK, Singh S. Quasi injective and pseudo injective modules. Canadian Mathematical Bulletin. 1975;18(3):359-366.
  5. Noyan Er, Singh S, Srivastava AK. Rings and modules which are stable under automorphisms of their injective hulls. J Algebra 379. 2013:223-229.
  6. Eisenbud D, Griffith P. Serial rings. Journal of Algebra. 1971;17(3):389-400.
  7. Goodearl KR, Warfield JRB. An Introduction to Noncommutative Noetherian Rings. 2 ed. Cambridge: Cambridge University Press; 2004.
  8. Fuller KR. On indecomposable injectives over artinian rings. Pacific J Math. 1969;29(1):115-135.
  9. Mohamed SH, Muller BJ. Continuous and Discrete Modules. Cambridge: Cambridge University Press; 1990.
  10. Lenagan TH. Bounded hereditary noetherian prime rings. J London Math Soc 6. 1973;S2-6(2):241-246.
  11. Eisenbud D, Robson JC. Hereditary Noetherian prime rings. Journal of Algebra. 1970;16(1):86-104.
  12. Quynh TC, Abyzov AN, Trang DT. Rings all of whose finitely generated ideals are automorphism-invariant. Journal of Algebra and Its Applications. 2021:2250159.
  13. Goodearl KR. Von Neumann Regular Rings. Krieger Florida: Publishing Company; 1991.
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