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Prime Submodules and Flat Modules

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Abstract

In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also given.

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References

  1. Lu, C. P.: Prime submodules of modules. Comment. Math. Univ. St. Paul, 33(1), 61–69 (1984)

    MathSciNet  Google Scholar 

  2. McCasland, R. L., Moore, M. E.: Prime submodules. Comm. Algebra, 20(6), 1803–1817 (1992)

    MathSciNet  Google Scholar 

  3. Lu, C. P.: Spectra of modules. Comm. Algebra, 23(10), 3741–3752 (1995)

    MathSciNet  Google Scholar 

  4. Marcelo, A., Masque, M.: Prime submodule, the descent invariant, and module of finite length. Journal of Algebra, 189, 273–293 (1997)

    Article  MathSciNet  Google Scholar 

  5. George, A. M., McCasland, R. L., Smith, P. F.: A principal ideal theorem analogue for modules over commutative rings. Comm. Algebra, 22, 2083–2099 (1994)

    MathSciNet  Google Scholar 

  6. Larsen, M. D., McCarthy, P. J.: Multiplicative theory of ideals, Academic press, Inc., New York, 1971

  7. Matsumura, H.: Commutative ring theory, Cambridge University Press, Cambridge, 1992

  8. Azizi, A.: Intersectin of prime submodules and dimension of modules. Acta Math. Scientia, 25B(3), 385–394 (2005)

    MathSciNet  Google Scholar 

  9. Azizi, A., Sharif, H.: On prime submodules. Honam Mathematical Journal, 21(1), 1–12 (1999)

    MathSciNet  Google Scholar 

  10. Azizi, A.: Weak multiplication modules. Czech Mathematical Journal, 53(128), 529–534 (2003)

    Article  MathSciNet  Google Scholar 

  11. Sharp, R. Y.: Steps in Commutative Algebra, Cambridge University Press, Cambridge, 1990

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Azizi, A. Prime Submodules and Flat Modules. Acta Math Sinica 23, 147–152 (2007). https://doi.org/10.1007/s10114-005-0813-0

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  • DOI: https://doi.org/10.1007/s10114-005-0813-0

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