Poincaré series of modules over local rings
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- by Gerson Levin PDF
- Proc. Amer. Math. Soc. 72 (1978), 6-10 Request permission
Abstract:
There is a well known conjecture, originally made by Kaplansky, that the Poincaré series $P_R^M(z)$ of a finitely generated module M over a local ring R is a rational function. Two reductions of this conjecture are made, one to the case where M is artinian (for a fixed R) and the other to the case where R is artinian.References
- Tor Holtedahl Gulliksen, A proof of the existence of minimal $R$-algebra resolutions, Acta Math. 120 (1968), 53–58. MR 224607, DOI 10.1007/BF02394606
- Franco Ghione and Tor H. Gulliksen, Some reduction formulas for the Poincaré series of modules, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 58 (1975), no. 2, 82–91 (English, with Italian summary). MR 414545
- Gerson Levin, Local rings and Golod homomorphisms, J. Algebra 37 (1975), no. 2, 266–289. MR 429868, DOI 10.1016/0021-8693(75)90077-0
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 6-10
- MSC: Primary 13H99
- DOI: https://doi.org/10.1090/S0002-9939-1978-0503520-2
- MathSciNet review: 503520