Results 91 to 100 of about 194,411 (117)
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Journal of the London Mathematical Society, 2002
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 ...
Herzog, Jürgen +2 more
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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 ...
Herzog, Jürgen +2 more
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Rees algebras and their varieties
Publicationes Mathematicae Debrecen, 2022Following a paper of the reviewer [Publ. Inst. Math., Nouv. Sér. 29(43), 229-239 (1981; Zbl 0491.08002)], a subalgebra B of an algebra A is called a Rees subalgebra whenever there exists a congruence \(\theta\) on A such that \(\in \theta\) if and only if either \(x=y\) or both x, y are elements of B.
Chajda, Ivan, Duda, Jaromír
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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 ...
Singh, Priti, Kumar, Shiv Datt
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Rees algebras and gröbner bases
Communications in Algebra, 1990This paper deals with the following problem. Robbiano showed in [9] that standard bases, Grobner bases, Macaulay bases are all instances of the same general situation. In this paper, we develop this philosophy from the point of view of the Rees algebra R of a ring A w.r.t. a filtration F given on A.
PORTELLI, DARIO, SPANGHER, WALTER
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The S2-Closure of a Rees Algebra
Results in Mathematics, 1993In this article, the authors show the following: Theorem 1.3. Let \(A\) be a Noetherian ring with canonical module \(\omega_ A\), and suppose that \(A\) is generically a Gorenstein ring. Then \(B=\text{Hom}_ A(\omega_ A,\omega_ A)\) is the minimal extension of \(A\) with the property \((S_ 2)\). Theorem 1.6.
Noh, Sunsook, Vasconcelos, Wolmer V.
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Rees Algebras of a Class of Graded Ideals
Mathematical Notes, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Restuccia G., Utano R.
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On the structure of Noetherian symbolic rees algebras
Manuscripta Mathematica, 1990Let A be a Noetherian unmixed local ring, \(I\subset A\) an ideal, \(S\subset A\) a multiplicative system such that \(I\cap S=\emptyset\) and \(I^{(n)}:=A\cap I^ nA_ S\), \(n\in {\mathbb{Z}}\). If \(\ell (I^{(n)})=ht(I^{(n)})\) for a certain \(n\geq 1\), \(\ell (I)\) denotes the analytic spread of I, then the ring \(R_ I:=\oplus_{n\geq 0}I^{(n)} \) is ...
Goto, S. +3 more
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On the Betti numbers and Rees algebras of ideals with linear powers
Journal of Algebraic Combinatorics, 2021Lisa Nicklasson
exaly
On the Complete Integral Closure of the Rees Algebra
2019GABELLI STEFANIA, GUERRIERI, ANNA
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