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Reduction in Rees Algebra of Modules
Algebras and Representation Theory, 2014\textit{P. Eakin} and \textit{A. Sathaye} [J. Algebra 41, 439--454 (1976; Zbl 0348.13012)] proved that if \(I\) is an ideal in the local ring \(R\) with infinite residue field such that \(I^n\) can be generated by fewer than \(n+r \choose r\) elements, for some integers \(n\geq 1\) and \(r\geq 0\), then there are elements \(y_1,\dots,y_r\) in \(I ...
Shiv Datt Kumar
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A D-modules approach on the equations of the Rees algebra
Journal of Commutative Algebra, 2022 Let I subset of R = F[x(1), x(2)] be a height two ideal minimally generated by three homogeneous polynomials of the same degree d, where F is a field of characteristic zero.
Yairon Cid-Ruiz
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On the depth of the Rees algebra of an ideal module
Journal of Algebra, 2010 We study the Rees algebra R(E):=S(E)/τR(S(E)) of an ideal module E⊂G≃Re. We use the technique of Bourbaki ideals introduced by Simis, Ulrich and Vasconcelos (2003) [22] to relate the Rees algebra of a module E to the Rees algebra of an ideal I=I(E)⊂R ...
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Summary: Let \(B = k[x_1, \ldots, x_n]\) be a polynomial ring over a field \(k\) , and let \(A\) be a quotient ring of \(B\) by a homogeneous ideal \(J\) . Let \(\mathfrak{m}\) denote the maximal graded ideal of \(A\) . Then the Rees algebra \(R = A[{\mathfrak{m}} t]\) also has a presentation as a quotient ring of the polynomial ring \(k[x_1, \ldots ...
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