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Rings of Formal Power Series

Published online by Cambridge University Press:  20 November 2018

N. Sankaran
N. Sankaran*
Affiliation:
Queen's University, Kingston, Ontario; Panjab University, Chandigarh, India
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In this brief exposition we collect several results on rings of formal power series with coefficients from a field or a ring with some special properties. The results that are catalogued below are mostly algebraic in nature.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 207 - 220
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Ax, J. and Kochin, S., Diophantine problems on local fields: decidable fields, Ann. of Math. 83 (1966), 437-456.Google Scholar
2. Cashwell, E. D., and Everett, C. J., The ring of number theoretic functions, Pacific J. Math. 9 (1959), 975-985.Google Scholar
3. Chevalley, C., On the theory of local rings, Trans. Amer. Math. Soc. 44 (1943), 690-708.Google Scholar
4. Chevalley, C., Some properties of ideals in rings of power series, Trans. Amer. Math. Soc. 45 (1944), 68-84.Google Scholar
5. Chevalley, C., Intersections of algebraic and algebroid varieties, Trans. Amer. Math. Soc. 47 (1945), 1-85.Google Scholar
6. Cohen, I. S., Structure of complete local rings, Trans. Amer. Math. Soc. 49 (1946), 54-106.Google Scholar
7. Deckard, D. and Durst, L. K., Unique factorization in power series rings and semigroups, Pacific J. Math. 16 (1966), 239-242.Google Scholar
8. Gerstenhaber, M., On the deformations of rings and algebras, Ann. of Math. 79 (1964), 59-103.Google Scholar
9. Gilmer, R., A note on the quotient field of the domain D[[x]], Proc. Amer. Math. Soc. 18 (1966), 1138-1140.Google Scholar
10. Gilmer, R. and Heinzer, , Rings of formal power series over a Krull domain, Notices Amer. Math. Soc. (1967), p. 27.Google Scholar
11. Gilmer, R., Integral dependence in power series rings, J. Algebra, 11 (1969), 488-502.Google Scholar
12. Gilmer, R., Power series rings over a Krull domain, Pacific J. Math. 29 (1969), 543-549.Google Scholar
13. Gilmer, R., R-automorphisms of R[[x]], Notices Amer. Math. Soc, (1969), p. 1043.Google Scholar
14. Krull, W., Beitrage zur Arithmetik kommutativa integifatsberiche, Math. Z. 43 (1938), 768-782.Google Scholar
15. Krull, W., Jacobsonche Ringe, Hilbertscher Nullstellensatz, Dimensiones Theorie. Math. Z. (1951), 354-387.Google Scholar
16. Lafon, J. P., Théorème de préparation de Weierstrass et Séries formelles Algébraiques, Univ. do Recife 11 (1966).Google Scholar
17. Lang, S., Quasi algebraic closure, Ann. of Math. 55 (1952), 367-390.Google Scholar
18. Malgrange, B., Cartan seminar, 1963.Google Scholar
19. Nagata, M., Local rings, Interscience, New York, Vol. 13.Google Scholar
20. Ohm, J., Some counter examples related to integral closure, Trans. Amer. Math. Soc. 121 (1966), 321-336.Google Scholar
21. O'Malley, M. J., R-automorphisms of R[[x]]. Proc. London Math. Soc, 1970.Google Scholar
22. Rückert, W., Zum Eliminations problem der Potenzreihenideale, Math. Ann. 107 (1932).Google Scholar
23. Salmon, P., Sur les series formelles restraintes, Bull. Math. Soc, France, 92 (1964), 385-410.Google Scholar
24. Samuel, P., On unique factorization domains, Illinois J. Math. 5 (1961), 1-17.Google Scholar
25. Samuel, P., On unique factorization domain, TIFR notes.Google Scholar
26. Samuel, P., Sur les anneaux factoriels, Bull. Soc. Math., France, 89 (1961), 155-173.Google Scholar
27. Samuel, P., Groupes finis d'automorphismes des anneaux de series formelles, Bull. Sci. Math. 90(1966), 97-101.Google Scholar
28. Sankaran, N., A theorem on Henselian Rings, Canad. Math. Bull., 1968.Google Scholar
29. Sankaran, N., Some Remarks on Weierstrass Preparation Theorem, Queen's Preprint.Google Scholar
30. Sankaran, N., R-automorphisms of the ring of restricted power series over R, Notices Amer. Math. Soc (1969), p. 799.Google Scholar
31. Soublin, J. P., Anneaux coherents, C. R. Acad. Sc 267 (1968), 183-186.Google Scholar
32. Soublin, J. P., Anneaux uniformement coherents, C. R. Acad. Sc. 267 (1968). 205-208.Google Scholar
33. Soublin, J. P., Un anneau cohérent dout Vanneau des polyn?mes n 'est pas cohérent, C. R. Acad. Sc 267 (1968), 241-243.Google Scholar
34. Terjanian, G., Sur les Corps finis, C. R. Acad., Paris, 262 (1965), 167-169.Google Scholar
35. Walker, R. J. T., Algebraic curves, Dover, New York, 1962.Google Scholar
36. Weil, A., Basic number theory, Springer-Verlag, New York, 1967.Google Scholar
37. Zariski, O., On equi singularities, Amer. J. Math. 87 (1966), 507-536.Google Scholar
38. Zariski, O. and Samuel, P., Commutative algebra, Vol. 2, Van Nostrand, Princeton, N.J., 1960.Google Scholar