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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Finite modules and algebras over Dedekind domains and analytic number theory


Author: John Knopfmacher
Journal: Bull. Amer. Math. Soc. 78 (1972), 193-196
MSC (1970): Primary 13C10, 13E10, 13F05, 16A22, 16A40, 16A44, 16A46, 17B99; Secondary 10H25, 10H40, 10J20, 12A70, 12A75
DOI: https://doi.org/10.1090/S0002-9904-1972-12910-0
MathSciNet review: 0289563
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  • 1. F. C. Auluck and C. B. Haselgrove, On Ingham's Tauberian theorem for partitions, Proc. Cambridge Philos. Soc. 48 (1952), 566-570. MR 14, 138. MR 49228
  • 2. J. Ax, Elementary theory of finite fields, Ann. of Math. (2) 88 (1968), 239-271. MR 37 #5187. MR 229613
  • 3. N. A. Brigham, A general asymptotic formula for partition functions, Proc. Amer. Math. Soc. 1 (1950), 181-191. MR 11, 582. MR 34409
  • 4. P. Erdös and G. Szekeres, Über die Anzahl der Abelschen Gruppen gegebener Ordnung und über ein verwandtes zahlentheoretisches Problem, Acta Sci. Math. Szeged 7 (1935), 95-102.
  • 5. G. H. Hardy and S. Ramanujan, Asymptotic formulae concerning the distribution of integers of various types, Proc. London Math. Soc. (2) 16 (1917), 112-132.
  • 6. G. Higman, Enumerating p-groups. I, Proc. London Math. Soc. (3) 10 (1960), 24-30. MR 22 #4779. MR 113948
  • 7. A. E. Ingham, A Tauberian theorem for partitions, Ann. of Math. (2) 42 (1941), 1075-1090. MR 3, 166. MR 5522
  • 8. N. Jacobson, Theory of rings, Math. Surveys, no. 2, Amer. Math. Soc. Providence, R.I., 1943. MR 5, 31. MR 8601
  • 9. I. Kaplansky, Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc. 72 (1952), 327-340. MR 13, 719. MR 46349
  • 10. J. Knopfmacher, Arithmetical properties of finite rings and algebras, and analytic number theory, Bull. Amer. Math. Soc. 76 (1970), 830-833. MR 274529
  • 11. J. Knopfmacher, Arithmetical properties of finite rings and algebras, and analytic number theory, J. Reine Angew. Math, (to appear). MR 274529
  • 12. R. L. Kruse and D. T. Price, Nilpotent rings, Gordon and Breach, New York, 1969. MR 42 # 1858. MR 266956
  • 13. E. Landau, Einführung in die elementare und analytische Theorie der algebraischen Zahlen und der Ideale, Chelsea, New York, 1949. MR 11, 85. MR 31002
  • 14. J.-P. Serre, Corps locaux, Actualités Sci. Indust., no. 1296, Hermann, Paris, 1962. MR 27 #133. MR 150130
  • 15. H. Wegmann, Beiträge zur Zahlentheorie auf freien Halbgruppen. I, II, J. Reine Angew. Math. 221 (1965), 20-43; 150-159. MR 32 #4097; #4098. MR 186639

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DOI: https://doi.org/10.1090/S0002-9904-1972-12910-0

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