Buradasınız

Anasayfa » Content

Some Remarks on Finitely Quasi-injective Modules

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2013

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
Let R be a ring. A right R-module M is called finitely quasi-injective if each R-homomorphism from a finitely generated submodule of M to M can be extended to an endomorphism of M. Some conditions under which finitely generated finitely quasi-injective modules are of finite Goldie Dimensions are given, and finitely generated finitely quasi-injective Kasch modules are studied.
Bookmark/Search this post with
FULL TEXT (PDF): 
PDF icon 1767-4204-1-pb.pdf
  • 2
119-125
  • English

REFERENCES

References: 

[1] T. Albu and R. Wisbauer. Kasch modules. In S. K. Jain and S. T. Rizvi, editors, Advances
in Ring Theory, pages 1–16, 1997.
[2] J. L. Chen, N. Q. Ding, Y. L. Li, and Y. Q. Zhou. On (m, n)-injectivity of modules.
Communications in Algebra, 29:5589–5603, 2001.
[3] J. L. Chen, N. Q. Ding, and M. F. Yousif. On generalizations of PF-rings. Communications
in Algebra, 32:521–533, 2004.
[4] A. Facchini. Module Theory, Endomorphism rings and direct sum decompositions in some
classes of modules. Birkhäuser Verlag, Basel, 1998.
[5] W. K. Nicholson, J. K. Park, and M. F. Yousif. Principally quasi-injective modules. Communications
in Algebra, 27:1683–1693, 1999.
[6] S. Page and Y. Q. Zhou. Generalization of principally injective rings. Journal of Algebra,
206:706–721, 1998.
REFERENCES 125
[7] V. S. Ramamurthi and K. M. Rangaswamy. On finitely injective modules. Journal of the
Australian Mathematical Society, 16:239–248, 1973.
[8] L. Shen and J. L. Chen. On strong goldie dimension. Communications in Algebra,
35:3018–3025, 2007.
[9] G. S. Xiao, X. B. Yin, and W. T. Tong. A note on AP-injective rings. Journal of Mathematical
Research & Exposition, 35:211–216, 2003.
[10] Z. M. Zhu. Finitely quasi-injective modules. Journal of Shandong University (Nat. Sci.),
45:20–23, 2010.
[11] Z. M. Zhu. MP-injective rings and MGP-injective rings. Indian Journal of Pure & Applied
Mathematics, 41:627–645, 2010.

Thank you for copying data from http://www.arastirmax.com