Geodesic
On asymptotic values of certain sets of attached prime ideals
Glasgow mathematical journal, Tome 30 (1988) no. 3, pp. 293-300

Voir la notice de l'article provenant de la source Cambridge University Press

In his paper [1], M. Brodmann showed that if M is a1 finitely generated module over the commutative Noetherian ring R (with identity) and a is an ideal of R then the sequence of sets {Ass(M/anM)}n∈N and {Ass(an−1M/anM)}n∈N (where N denotes the set of positive integers) are eventually constant. Since then, the theory of asymptotic prime divisors has been studied extensively: in [5], Chapters 1 and 2], for example, various results concerning the eventual stable values of Ass(R/an;) and Ass(an−1/an), denoted by A*(a) and B*(a) respectively, are discussed. It is worth mentioning that the above mentioned results of Brodmann still hold if one assumes only that A is a commutative ring (with identity) and M is a Noetherian A-module, and AssA(M), in this situation, is regarded as the set of prime ideals belonging to the zero submodule of M for primary decomposition. 
Taherizadeh, A.-J. On asymptotic values of certain sets of attached prime ideals. Glasgow mathematical journal, Tome 30 (1988) no. 3, pp. 293-300. doi: 10.1017/S0017089500007382
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[1] 1.Brodmann, M., Asymptotic stability of Ass(M/InM), Proc. Amer. Math. Soc. 74 (1979), 16–18. Google Scholar

[2] 2.Kirby, D., Artinian modules and Hilbert polynomials, Quart. J. Math. Oxford Ser. (2) 24 (1973), 47–57. Google Scholar | DOI

[3] 3.Kirby, D., Coprimary decomposition of Artinian modules, J. London Math. Soc. (2) 6 (1973), 571–576. Google Scholar | DOI

[4] 4.Macdonald, I. G., Secondary representation of modules over a commutative ring, Symposia Mathematica 11 (1973), 23–43. Google Scholar

[5] 5.McAdam, S., Asymptotic prime divisors, Lecture Notes in Mathematics 1023 (Springer, 1983). Google Scholar | DOI

[6] 6.Northcott, D. G., Generalized Koszul complexes and Artinian modules, Quart. J. Math. Oxford Ser. (2) 23 (1972), 289–297. Google Scholar | DOI

[7] 7.Sharp, R. Y., Asymptotic behaviour of certain sets of attached prime ideals, J. London Math. Soc. (2) 34 (1986), 212–218. Google Scholar | DOI

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