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On the ring of Hurwitz series.(English)Zbl 0884.13013

Author’s abstract: This paper introduces the ring of Hurwitz series over a commutative ring with identity, and examines its structure and applications, especially to the study of differential algebra. In particular, we see that rings of Hurwitz series bear a resemblance to rings of formal power series, and that for rings of positive characteristic, the structure of the ring of Hurwitz series closely mirrors that of the ground ring.

MSC:

13N05 Modules of differentials
13F25 Formal power series rings
13A35 Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure

Cite

References:

[1]Bochner, S. and Martin, W.T. 1937.Singularities of composite functions in several variables, Vol. 38, 293–302. Annals of Math. ·Zbl 0016.31103
[2]Eisenbud D., Commutative Algebra with a View Toward Algebraic Geometry (1995) ·Zbl 0819.13001
[3]Fields, D.E. 1971.Zero divisors and nilpotent elements in power series rings, Vol. 27, 427–433. Proc. Amer. Math. Soc. ·Zbl 0219.13023
[4]Fliess, M. 1947.Sur divers produits de séries formelles, Vol. 102, 181–191. France: Bull. Soc. Math. ·Zbl 0313.13021
[5]Hurwitz, A. 1899.Sur un théorème de M. Hadamard, Vol. 128, 350–353. C.R. Acad. Sc. ·JFM 30.0362.03
[6]Keigher, W.F. 1975.Adjunctions and comonads in differential algebra, Vol. 59, 99–112. Pacific J. Math. ·Zbl 0327.12104
[7]Keigher, W.F. 1978.Quasi-prime ideals in differential rings, Vol. 4, 379–388. Houston J. Math. ·Zbl 0402.13020
[8]Keigher, W.F. 1982.Differential rings constructed from quasi-prime ideals, Vol. 26, 191–201. J. Pure and Appl. Algebra. ·Zbl 0511.13016
[9]Keigher W.F., Quasiradical ideals in differential rings, in preparation
[10]Kolchin E., Differential Algebra and Algebraic Groups (1973) ·Zbl 0264.12102
[11]Sweedler M., Hopf Algebras (1968)
[12]Taft, E.J. 1990.Hurwitz invertibility of linearly recursive sequences, Vol. 73, 37–40. Congressurn Numemntium. ·Zbl 0694.16006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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