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.
Similar content being viewed by others
References
Lu, C. P.: Prime submodules of modules. Comment. Math. Univ. St. Paul, 33(1), 61–69 (1984)
McCasland, R. L., Moore, M. E.: Prime submodules. Comm. Algebra, 20(6), 1803–1817 (1992)
Lu, C. P.: Spectra of modules. Comm. Algebra, 23(10), 3741–3752 (1995)
Marcelo, A., Masque, M.: Prime submodule, the descent invariant, and module of finite length. Journal of Algebra, 189, 273–293 (1997)
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)
Larsen, M. D., McCarthy, P. J.: Multiplicative theory of ideals, Academic press, Inc., New York, 1971
Matsumura, H.: Commutative ring theory, Cambridge University Press, Cambridge, 1992
Azizi, A.: Intersectin of prime submodules and dimension of modules. Acta Math. Scientia, 25B(3), 385–394 (2005)
Azizi, A., Sharif, H.: On prime submodules. Honam Mathematical Journal, 21(1), 1–12 (1999)
Azizi, A.: Weak multiplication modules. Czech Mathematical Journal, 53(128), 529–534 (2003)
Sharp, R. Y.: Steps in Commutative Algebra, Cambridge University Press, Cambridge, 1990
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Azizi, A. Prime Submodules and Flat Modules. Acta Math Sinica 23, 147–152 (2007). https://doi.org/10.1007/s10114-005-0813-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-005-0813-0