Skip to main content
Log in

RETRACTED ARTICLE: On graded distributive modules

  • Published:
Mathematical Notes Aims and scope Submit manuscript

This article was retracted on 01 July 2017

Abstract

Let R be a ℤ-graded commutative ring with identity. Several characterizations of graded distributive modules will be investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T. M. K. Davison, “Distributive homomorphism of rings and modules,” J. Reine Angew. Math. 270, 28–34 (1974).

    MathSciNet  MATH  Google Scholar 

  2. W. Stephenson, “Modules whose lattice of submodules is distributive,” Proc. London Math. Soc. (3) 28, 291–310 (1974).

    Article  MathSciNet  Google Scholar 

  3. V. Erdoğdu, “Distributive modules,” Canad. Math. Bull. 30(2), 248–254 (1987).

    Article  MathSciNet  Google Scholar 

  4. V. Erdoğdu, “The distributive hull of a ring,” J. Algebra 132(2), 263–269 (1990).

    Article  MathSciNet  Google Scholar 

  5. V. Erdoğou, “Cyclically decomposable distributive modules,” Comm. Algebra 25(5), 1635–1639 (1997).

    Article  MathSciNet  Google Scholar 

  6. A. A. Tuganbaev, Semidistributive Modules and Rings, in Mathematics and Its Applications, Vol. 449 (Klüwer Academic, Dordrecht-Boston-London, 1998).

    Google Scholar 

  7. A. A. Tuganbaev, Distributive Modules and Related Topics, in Algebra, Logic, and Applications, Vol. 12 (Gordon & Breach, Amsterdam, 1999).

    Google Scholar 

  8. J. Escoriza and B. Torrecillas, “Multiplication objects in commutative Grothendieck categories,” Comm. Algebra 26(6), 1867–1883 (1998).

    Article  MathSciNet  Google Scholar 

  9. R. Naghipour and N. Zamani, “Graded distributive modules,” Southeast Asian Bull. Math. 29(6), 1095–1099 (2005).

    MathSciNet  MATH  Google Scholar 

  10. C. Nastasescu and F. van Oystaeyen, Graded Ring Theory, in North-Holland Mathematical Library, Vol. 28 (North-Holland Publishing Co., Amsterdam-New York, 1982).

    Google Scholar 

  11. D. H. Underwood, “On some uniqueness questions in primary representations of ideals,” J. Math. Kyoto Univ. 9, 69–94 (1969).

    Article  MathSciNet  Google Scholar 

  12. M. D. Larsen and P. J. McCarthy, Multiplicative Theory of Ideals, in Pure and Applied Mathematics, Vol. 43 (Academic Press, New York-London, 1971).

    Google Scholar 

  13. R. A. Kuntz, “Associated prime divisors in the sense of Krull,” Canad. J. Math. 24, 808–818 (1972).

    Article  MathSciNet  Google Scholar 

  14. W. Bruns and J. Herzog, Cohen-Macaulay Rings, in Cambridge Studies in Advanced Mathematics, Vol. 39 (Cambridge Univ. Press, Cambridge, 1998).

    Google Scholar 

  15. S. Goto and K. Watanabe, “On graded rings. I,” J. Math. Soc. Japan 30(2), 179–213 (1978).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Zamani.

Additional information

Published in Russian in Matematicheskie Zametki, 2008, Vol. 83, No. 4, pp. 528–535.

The text was submitted by the author in English.

N. Zamani On graded distributive modules Mathematical Notes (2008) 83:485 DOI: 10.1134/S0001434608030218

Following the retraction of the article the author informed the Editor in Chief and the publisher that the duplicate publication of this article was not caused by duplicate submission.

The author stated that the article "Characterizations of Graded Distributive Modules", [Journal of Applied Mathematics (2008), vol. 16, iss. 5] was published without his knowledge.

An erratum to this article can be found online at http://dx.doi.org/10.1134/S000143461707015X.

About this article

Cite this article

Zamani, N. RETRACTED ARTICLE: On graded distributive modules. Math Notes 83, 485–491 (2008). https://doi.org/10.1134/S0001434608030218

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434608030218

Key words

Navigation