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Currently displaying 1 – 3 of 3

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A splitting theorem for ℱ-products

Philippe Loustaunau — 1990

Fundamenta Mathematicae

The prime spectrum of an infinite product of copies of Z

Ronnie Levy; Philippe Loustaunau; Jay Shapiro — 1991

Fundamenta Mathematicae

Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring

William W. Adams; Philippe Loustaunau; Victor P. Palamodov; Daniele C. Struppa — 1997

Annales de l'institut Fourier

In this paper we prove that the projective dimension of $ℳ_{n} = R^{4} / ⟨ A_{n} ⟩$ is $2 n - 1$ , where $R$ is the ring of polynomials in $4 n$ variables with complex coefficients, and $⟨ A_{n} ⟩$ is the module generated by the columns of a $4 \times 4 n$ matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of $n$ quaternionic variables. As a corollary we show that the sheaf $ℛ$ of regular functions has flabby dimension $2 n - 1$ , and we prove a cohomology vanishing theorem for open...

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