Some results on prime and primary submodules
DOI:
https://doi.org/10.4067/S0716-09172003000300003Keywords:
Prime and Primary Submodules, Radical of Submodules, Rees Algebra of Modules.Abstract
This article is devoted to study some properties of prime and primary submodules. First we characterize prime submodules of free modules and give a primality condition for certain submodules in terms of associated prime ideals. Furthermore, by using symmetric algebra of modules we describe Rees algebras associated to prime submodules and provide a computational method to check if some primary submodules of a free module have prime radical.
References
[1] C.-P. Lu, “Spectra of Modules” Comm. Alg. 23, pp. 3741-3752, (1995).
[2] A. Marcelo and J. Muñoz, “Prime Submodules, the Descent Invariant, and Modules of Finite Length”, J. Alg. 189, pp. 273 - 293, (1997).
[3] A. Marcelo and C. Rodríguez, “Radicals of Submodules and Symmetric Algebra”, Comm. Alg. 28 (10), pp. 4611-4617, (2000).
[4] H. Matsumura, “Commutative Ring Theory”, Cambridge Univ. Press, (1986).
[5] R.McCasland and M. Moore, “Prime Submodules”, Comm. Alg. 20
(6), pp. 1803-1817, (1992).
[6] D. Pusat-Yilmaz and P. Smith, “Radicals of Submodules of Free Modules”, Preprint, Univ. of Glasgow, (1997).
[7] P. Smith, “Primary Modules over Commutative Rings”, Preprint, Univ. of Glasgow, (1999).
[8] W. Vasconcelos,“Arithmetic of Blowup Algebras”, Cambridge University Press, (1994).
[2] A. Marcelo and J. Muñoz, “Prime Submodules, the Descent Invariant, and Modules of Finite Length”, J. Alg. 189, pp. 273 - 293, (1997).
[3] A. Marcelo and C. Rodríguez, “Radicals of Submodules and Symmetric Algebra”, Comm. Alg. 28 (10), pp. 4611-4617, (2000).
[4] H. Matsumura, “Commutative Ring Theory”, Cambridge Univ. Press, (1986).
[5] R.McCasland and M. Moore, “Prime Submodules”, Comm. Alg. 20
(6), pp. 1803-1817, (1992).
[6] D. Pusat-Yilmaz and P. Smith, “Radicals of Submodules of Free Modules”, Preprint, Univ. of Glasgow, (1997).
[7] P. Smith, “Primary Modules over Commutative Rings”, Preprint, Univ. of Glasgow, (1999).
[8] W. Vasconcelos,“Arithmetic of Blowup Algebras”, Cambridge University Press, (1994).
Published
2017-04-24
How to Cite
[1]
A. M. Vega, F. M. Wirnitzer, and C. Rodríguez Mielgo, “Some results on prime and primary submodules”, Proyecciones (Antofagasta, On line), vol. 22, no. 3, pp. 201-208, Apr. 2017.
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