A Note on Artinian Primes and Second Modules

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

 Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

Keywords


[1] F. Anderson and K. Fuller, Rings and categories of modules, Graduate Text in Mathematics, Springer-
Verlag, Berlin- New York, 1974.
[2] A. Azizi and H. Sharif, On Prime Submodules, Honam, Mathematical Journal, 21(1) (1999), 1-12
[3] M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra. Addision-Wesley Publishing Com-
pany, Inc, 1969.
[4] J. Dauns, Prime Modules, J. Reine angew Math 298 (1978), 156-181.
[5] E. H. Feller and E. W. Swokowski, Prime Modules, Canad. J. Math. 17 (1965), 1041-1052.
[6] T. W. Hungerford, Algebra, Springer-Verlog, New York Inc, 1989.
[7] C. P. Lu, Prime Submodules of Modules, Comm. Math. Univ. Sancti. Pauli, 33 (1984), 61-69
[8] C. P. Lu, Spectra of modules, Comm-Algebra, 23 (10), (1995), 3741-3752.
[9] R. L. Mccaslad and M. E. Moore, Prime Submodules, Comm. Algebra, 20 (6) (1992), 1803-1817.
[10] H. Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, 1992.
[11] S. Namazi and Y. Sharifi, Catenary Modules, Acta Math, Hungarica, 85 (3) (1999), 211-218.
[12] R. Y. Sharp, A Method for the study of artinian modules, with an application to asymtotic behavior, math.
Sci. Res. Ins. Publ. 15 (1989), 443-465,Springer-Verlag
[13] R. Y. Sharp, Steps in commutative Algebra, Cambridge University Press 1990.
[14] Y. Tiras and M. Alkan, Prime modules and submodules, Comm. Algebra, 31 (11) (2003), 5253-5261.