Results 11 to 20 of about 4,993 (263)

Filtrations, rees rings, and ideal transforms

Journal of Pure and Applied Algebra, 1986
Let I, J be ideals and S a multiplicatively closed set of a Noetherian ring R. \textit{P. Schenzel} [''Finiteness of relative Rees rings and asymptotic prime divisors'' (preprint)] has studied the graded extension ring \({\mathcal R}(f(I,J))\) of the Rees ring \({\mathcal R}(I)=\oplus^{\infty}_{-\infty}I^ n\quad whose\) n-th component is \(\cup_{m}(I ...
McAdam, Stephen
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Integral closures of ideals in the Rees ring [PDF]

Colloquium Mathematicum, 1993
Let \(R\) be a commutative Noetherian ring, \(I\) an ideal of \(R\) and \({\mathcal R} = R[It,t^{- 1}]\) the Rees ring of \(R\) with respect to \(I\). Let \(M\) be a Noetherian \(R\)-module and \[ \mathbb{M} = R(M,I) = \{\sum^s_{i = - r} m_i t^i \in M [t,t^{- 1}]: m_i \in I^i M\}. \] Then \(({\mathcal R} t^{- k})^{- (\mathbb{M})} \cap R = (I^k)^{- (M)}\
Tiraş, Y.
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Bases of ideals and Rees valuation rings

Journal of Algebra, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heinzer, William J., Ratliff, Louis J., Rush, David E.   +2 more
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Rees cones and monomial rings of matroids

Linear Algebra and its Applications, 2008
Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring.
Villarreal, Rafael H.
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Segre and Rees products of posets, with ring-theoretic applications

Journal of Pure and Applied Algebra, 2005
We introduce (weighted) Segre and Rees products for posets and show that these constructions preserve the Cohen-Macaulay property over a field $k$ and homotopically. As an application we show that the weighted Segre product of two affine semigroup rings that are Koszul is again Koszul. This result generalizes previous results by Crona on weighted Segre
Björner, Anders, Welker, Volkmar
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Duality and the equations of Rees rings and tangent algebras

Mathematische Nachrichten
AbstractLet be a module of projective dimension 1 over a Noetherian ring and consider its Rees algebra . We study this ring as a quotient of the symmetric algebra and consider the ideal defining this quotient. In the case that is a complete intersection ring, we employ a duality between and in order to study the Rees ring in multiple settings ...
Weaver, Matthew
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Ore-Rees rings which are maximal orders

Journal of the Mathematical Society of Japan, 2016
Ore-Rees rings are defined as combinations of twisted polynomial rings \(R[t;\sigma,\delta]\) over a Noetherian prime ring \(R\) and Rees rings over \(R\) with respect to a \(\sigma\)-invariant invertible ideal \(X\). Thus, an Ore-Rees ring \(S\) is of the form \(S=R\oplus Xt\oplus Xt^2\oplus\cdots\), viewed as a subring of \(R[t;\sigma,\delta]\).
HELMI, Monika R., MARUBAYASHI, Hidetoshi, UEDA, Akira   +2 more
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Quasi-Unmixedness and Integral Closure of Rees Rings [PDF]

Proceedings of the American Mathematical Society, 1976
For certain Rees rings R \mathcal {R} of a local domain
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Note on ideal-transforms, Rees rings, and Krull rings

Journal of Algebra, 1987
The main result gives several necessary and sufficient conditions for the ideal transform T(I) to be finitely generated over R, when I is a height one ideal in an important class of two-dimensional local rings R. One of these conditions is that the integral closure of T(I) coincides with the complete integral closure of T(I). Then it is shown that if I
Eakin, Paul M, Heinzer, William, Katz, Daniel, Ratliff, L.J   +3 more
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Asymptotic sequences and rees rings

Journal of Algebra, 1984
Let \(b_ 1,...,b_ s\) be an asymptotic sequence over an ideal I in a Noetherian ring R and let \(B_ i=(b_ 1,...,b_ i)R.\) Then it is shown that certain sequences closely related to these elements are asymptotic sequences over I\({\mathcal R}(R,B_ i)\), over tI\({\mathcal R}(R,I)\), and over u\({\mathcal R}(R,I)\), where \({\mathcal R}(R,J)\) is the ...
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