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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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Proceedings of the London Mathematical Society, 2003
Summary: We study Rees algebras of modules within a fairly general framework. We introduce an approach through the notion of Bourbaki ideals that allows the use of deformation theory. One can talk about the (essentially unique) generic Bourbaki ideal \(I(E)\) of a module \(E\) which, in many situations, allows one to reduce the nature of the Rees ...
Simis, Aron +2 more
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Summary: We study Rees algebras of modules within a fairly general framework. We introduce an approach through the notion of Bourbaki ideals that allows the use of deformation theory. One can talk about the (essentially unique) generic Bourbaki ideal \(I(E)\) of a module \(E\) which, in many situations, allows one to reduce the nature of the Rees ...
Simis, Aron +2 more
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Journal of Pure and Applied Algebra, 2023
Following [\textit{V. Barucci} et al., Commun. Algebra 43, No. 1, 130--142 (2015; Zbl 1327.13087); Ark. Mat. 54, No. 2, 321--338 (2016; Zbl 1372.13017)] the authors of the paper, investigate on a family of quadratic quotients of Rees algebras over a commutative ring.
Marco D'Anna +2 more
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Following [\textit{V. Barucci} et al., Commun. Algebra 43, No. 1, 130--142 (2015; Zbl 1327.13087); Ark. Mat. 54, No. 2, 321--338 (2016; Zbl 1372.13017)] the authors of the paper, investigate on a family of quadratic quotients of Rees algebras over a commutative ring.
Marco D'Anna +2 more
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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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Residual intersections and modules with Cohen-Macaulay Rees algebra
Journal of Algebra, 2021Alessandra Costantini
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Hilbert-Kunz function and Hilbert-Kunz multiplicity of some ideals of the Rees algebra
Communications in Algebra, 2021Kriti Goel, Jugal Verma
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A Family of Quotients of the Rees Algebra
Communications in Algebra, 2015Marco D’Anna, Francesco Strazzanti
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