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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.22 no.3 Antofagasta Dec. 2003

http://dx.doi.org/10.4067/S0716-09172003000300003 

Proyecciones
Vol. 22, N o 3, pp. 201-208, December 2003.
Universidad Católica del Norte
Antofagasta - Chile

SOME RESULTS ON PRIME AND PRIMARY
SUBMODULES

AGUSTÍN MARCELO
FÉLIX MARCELO
and
CÉSAR RODRÍIGUEZ
Universidad de Las Palmas de Gran Canaria, España

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 sub-modules
and provide a computational method to check if some primary
submodules of a free module have prime radical.

1991 Mathematical Subject Classification : Primary 13C13;
Secondary 13A10.

Key Words and Phrases : Prime and Primary Submodules,
Radical of Submodules, Rees Algebra of Modules.

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. Rodr ´ iguez, "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",CambridgeUniversity Press, (1994).

Received : January 2003.

Agustín MarceloVega
Departamento de Matemáticas
Campus de Tafira
35017 Las Palmas de Gran Canaria
España
e-mail : amarcelo@dma.ulpgc.es

Félix Marcelo Wirnitzer
Departamento de Matemáticas
Campus de Tafira
35017 Las Palmas de Gran Canaria
España
e-mail : wernitz@dma.ulpgc.es

and

César Rodríguez Mielgo
Departamento de Matemáticas
Campus de Tafira
35017 Las Palmas de Gran Canaria
España
e-mail : cesar@dma.ulpgc.es

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