Weak normalisation and the power series rings

Maloo, Alok Kumar

doi:10.1016/0022-4049(95)00158-1

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2000

2024

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Cited by 3 publications

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“…If one identifies a fonnal power series L~=o anx l1 E R [[x]] with the sequence of its coefficients (an), then multiplication in H R is similar to the usual product of formal power series, except that binolnial coefficients are introduced at each tenn in the product as follows. The Hurwitz product of (an) and (bn) is given by ( The rings of Hurwitz series have been of interest and have had ilnportant applications in Inany areas, for exalnple, in differential algebra (see [4] and [5]) and in the discussion about weak nonnalization ( [7]). This product of sequences using the binon1ial coefficients was studied in papers by Fleiss [2] and Taft [10].…”

Section: Introductionmentioning

confidence: 99%

Hermite and ps-rings of hurwitz series^∗

Liu¹

2000

Communications in Algebra

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Let R be a cOlllmutative ring and H R the ring of Hurwitz series over R. In this note, we consider sonle properties of rings, which are shared by Rand HR. In particular, we show that for the rings Rand H R, if either ring is (i) a Hennite ring, or (ii) a PF -ring in the sense that every finitely generated projective R-n10dule is free, then so is another. We also show that if R is a PS-ring in the sense that the socle Soc(RR)is projective and char(R) = 0, then H R is also a PS-ring.

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Section: Introductionmentioning

confidence: 99%