Titlebook: A Singular Introduction to Commutative Algebra; Gert-Martin Greuel,Gerhard Pfister Textbook 20021st edition Springer-Verlag Berlin Heidelb

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Partielle Differenzialgleichungen,es are in the centre of modern commutative algebra as a unifying approach. Formally, the notion of a module over a ring is the analogue of the notion of a vector space over a field, in the sense that a module is defined by the same axioms, except that we allow ring elements as scalars and not just f

exceptional

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https://doi.org/10.1007/978-3-540-73649-3latter rings contain informations about arbitrary small Zariski neighbourhoods of 0 ∈ .. Such neighbourhoods turn out to be still quite large, for instance, if . = 1 then they consist of . minus a finite number of points. If we are working over the field . = ℂ, respectively . = ℝ, we can use the con

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https://doi.org/10.1007/978-3-540-73649-3, the values of this function are given by a polynomial, the Hilbert polynomial. To show this, we use the Hilbert-Poincaré series, a formal power series in . with coefficients being the values of the Hilbert function. This power series turns out to be a rational function.

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