On Modules Having Small Cofinite Irreducibles
Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 490-494

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

In this paper we obtain several new characterizations of modules having small cofinite irreducibles. One of these characterizations involves a metric topology defined on the submodule lattice.
DOI : 10.4153/CMB-1994-071-4
Mots-clés : 13C05, 13E05, modules, local rings, submodules
Johnson, E. W.; Johnson, Johnny A. On Modules Having Small Cofinite Irreducibles. Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 490-494. doi: 10.4153/CMB-1994-071-4
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[1] 1. Anderson, D. D., The existence of dual modules, Proc. Amer. Math. Soc. 55(1976), 258–260. Google Scholar

[2] 2. Hochster, M., Cyclic purity versus purity in excellent Noetherian rings, Trans. Amer. Math. Soc. 231(1977), 463–487. Google Scholar

[3] 3. Johnson, E. W., Modules: duals and principally fake duals, Algebra Universalis 24(1987), 111–119. Google Scholar

[4] 4. Johnson, E. W. and Johnson, J. A., Lattice modules over semi-local Noether lattices, Fund. Math. 68(1970), 187–201. Google Scholar

[5] 5. Johnson, J. A. and Taylor, M. B., New characterizations of approximately Gorenstein rings, Glasgow Math. J. 34(1992), 361–363. 6.1. Kaplansky, Commutative rings, Allyn and Bacon, Boston, 1970. Google Scholar

[7] 7. Larsen, M. D. and McCarthy, P. J., Multiplicative Theorey of Ideals, Academic Press, New York and London, 1971. Google Scholar

[8] 8. Lu, Chin-Pi, Quasi-complete modules, Indiana Univ. Math. J. 29(1980), 277–286. Google Scholar

[9] 9. Nagata, M., Local rings, Interscience Tracts in Pure and Appl. Math. 13, Interscience, New York, 1962. Google Scholar

[10] 10. Northcott, D. G., Lessons on Rings, Modules and Multiplicities, Cambridge Univ. Press, London and New York, 1968. Google Scholar

[11] 11. Northcott, D. G. and Rees, D., Principal systems, Quart. J. Math. Oxford Ser. (2) 8(1957), 119–127. Google Scholar

[12] 12. Zariski, O. and Samuel, P., Commutative Algebra, Vol. II, Springer-Verlag, New York, 1960. Google Scholar

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