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c-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN

Year 2007, Volume: 2 Issue: 2 , 22 - 27 , 01.12.2007

Arshad Imam

https://izlik.org/JA45MP66XE

Abstract

In this paper we prove that every module over a Dedekind domain has a c-injective envelope.

Keywords

Complement (high) submodule c-injective module c-essential extension c-injective envelope

References

  • R.H. Alizade, K.D. Akıncı and A. Imam, On the structure of neat-injective envelopes, Mathematica (Cluj), 46 (69)2, 2004, 115-122.
  • L. Fuchs, Infinite Abelian Groups, Vol. 1, Academic Press, 1970.
  • A.I. Generalov, On weak and ω-high purity in the category of modules, Math. USSR, Sb., 34:1978, 345-356. Translated from Russian from Mat. Sb., N. Ser., 105(147) (1978), 389-402.
  • D.K. Harrison, J.M. Irwin, C.L. Peercy and E.A. Walker, High extension of abelian groups, Acta Math. Acad. Sci. Hungar., 14 (1963), 319-330.
  • A. Imam, Neat Injective Envelopes, Ph.D. Thesis, Dokuz Eyl¨ul University, ˙Izmir, Turkey, 2000.
  • E. Mermut, Homological Approach to Complements and Supplements, Ph.D. Thesis, Dokuz Eyl¨ul University, ˙Izmir, Turkey, 2004.
  • C. SantaClara and P.F. Smith, Modules which are self-injective relative to closed submodules, International Conference on Algebra and its Applications (Athens, OH, 1999), Contemp. Math., 259 (2000), 487-499.
  • B. Stenstr¨om, Pure submodules, Arkiv f¨or Matematik, 7(10) (1967), 159-171.
  • B. Stenstr¨om, High submodules and purity, Arkiv f¨or Matematik, 7(11) (1967), 173-176. Arshad Imam
  • Greenwich University, Karachi, Pakistan
  • E-mail: iarchad@hotmail.com

Year 2007, Volume: 2 Issue: 2 , 22 - 27 , 01.12.2007

Arshad Imam

https://izlik.org/JA45MP66XE

Abstract

References

  • R.H. Alizade, K.D. Akıncı and A. Imam, On the structure of neat-injective envelopes, Mathematica (Cluj), 46 (69)2, 2004, 115-122.
  • L. Fuchs, Infinite Abelian Groups, Vol. 1, Academic Press, 1970.
  • A.I. Generalov, On weak and ω-high purity in the category of modules, Math. USSR, Sb., 34:1978, 345-356. Translated from Russian from Mat. Sb., N. Ser., 105(147) (1978), 389-402.
  • D.K. Harrison, J.M. Irwin, C.L. Peercy and E.A. Walker, High extension of abelian groups, Acta Math. Acad. Sci. Hungar., 14 (1963), 319-330.
  • A. Imam, Neat Injective Envelopes, Ph.D. Thesis, Dokuz Eyl¨ul University, ˙Izmir, Turkey, 2000.
  • E. Mermut, Homological Approach to Complements and Supplements, Ph.D. Thesis, Dokuz Eyl¨ul University, ˙Izmir, Turkey, 2004.
  • C. SantaClara and P.F. Smith, Modules which are self-injective relative to closed submodules, International Conference on Algebra and its Applications (Athens, OH, 1999), Contemp. Math., 259 (2000), 487-499.
  • B. Stenstr¨om, Pure submodules, Arkiv f¨or Matematik, 7(10) (1967), 159-171.
  • B. Stenstr¨om, High submodules and purity, Arkiv f¨or Matematik, 7(11) (1967), 173-176. Arshad Imam
  • Greenwich University, Karachi, Pakistan
  • E-mail: iarchad@hotmail.com
There are 11 citations in total.

Details

Other ID JA84ZV95EY
Authors

Arshad Imam This is me

Publication Date December 1, 2007
IZ https://izlik.org/JA45MP66XE
Published in Issue Year 2007 Volume: 2 Issue: 2

Cite

APA Imam, A. (2007). c-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN. International Electronic Journal of Algebra, 2(2), 22-27. https://izlik.org/JA45MP66XE
AMA 1.Imam A. c-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN. IEJA. 2007;2(2):22-27. https://izlik.org/JA45MP66XE
Chicago Imam, Arshad. 2007. “C-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN”. International Electronic Journal of Algebra 2 (2): 22-27. https://izlik.org/JA45MP66XE.
EndNote Imam A (December 1, 2007) c-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN. International Electronic Journal of Algebra 2 2 22–27.
IEEE [1]A. Imam, “c-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN”, IEJA, vol. 2, no. 2, pp. 22–27, Dec. 2007, [Online]. Available: https://izlik.org/JA45MP66XE
ISNAD Imam, Arshad. “C-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN”. International Electronic Journal of Algebra 2/2 (December 1, 2007): 22-27. https://izlik.org/JA45MP66XE.
JAMA 1.Imam A. c-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN. IEJA. 2007;2:22–27.
MLA Imam, Arshad. “C-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN”. International Electronic Journal of Algebra, vol. 2, no. 2, Dec. 2007, pp. 22-27, https://izlik.org/JA45MP66XE.
Vancouver 1.Arshad Imam. c-INJECTIVE ENVELOPE OF MODULES OVER A DEDEKIND DOMAIN. IEJA [Internet]. 2007 Dec. 1;2(2):22-7. Available from: https://izlik.org/JA45MP66XE