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The w-integral closure of integral domains
Journal of Algebra, 2006 Let \(D\) be an integral domain with quotient field qf\((D)=K\). Recall that an element \(x \in K\) is called \(w\)-integral [respectively: pseudo-integral (or \(v\)-integral)] on \(D\) if \( xI^w \subseteq I^w\) [respectively: \(xI^v \subseteq I^v\)] for some nonzero finitely generated ideal \(I\) of \(D\). The authors denote by \(D^w\) [respectively:
Gyu Whan Chang, Muhammad Zafrullah
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Specialization and integral closure [PDF]
Journal of the London Mathematical Society, 2014 We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal. Also, with additional assumptions, we show that an element is integral over a module if it is integral modulo a generic element of the module ...
Jooyoun Hong, Bernd Ulrich
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Derivations and integral closure [PDF]
Pacific Journal of Mathematics, 1966 Let d? be an integral domain containing the rational numbers, Σ its quotient field, D a derivation of Σ, and &1 the ring of elements in Σ quasi-integral over &. It is shown that if £? then Dέ?f c &'.
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Integral Closures of Noetherian Integral Domains as Intersections [PDF]
Proceedings of the American Mathematical Society, 1995 Let \(A\) be a noetherian integral domain, \(\overline A\) its integral closure, and let \({\mathcal G}\) be the set of prime ideals \(P\) of \(A\) with height\((P) \leq 1\). The author provides three equivalent conditions for the equality \(\overline A = \bigcap \overline A_P\), \(P \in {\mathcal G}\). For instance, equality holds iff \(\bigcap A_P\),
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Triangular bases of integral closures [PDF]
Journal of Symbolic Computation, 2018 In this work, we consider the problem of computing triangular bases of integral closures of one-dimensional local rings. Let $(K, v)$ be a discrete valued field with valuation ring $\mathcal{O}$ and let $\mathfrak{m}$ be the maximal ideal. We take $f \in \mathcal{O}[x]$, a monic irreducible polynomial of degree $n$ and consider the extension $L = K[x]/(
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An Algorithm for Computing the Integral Closure
Journal of Symbolic Computation, 1998 In this article we give an algorithm for computing the integral closure of a reduced Noetherian ring R, in case this integral closure is finitely generated over R.
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Integral closures in real algebraic geometry
Journal of Algebraic Geometry, 2020 We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety: the regular functions and the continuous rational functions.
Fichou, Goulwen +2 more
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Computing Local Integral Closures
Journal of Symbolic Computation, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Closure facilitates contour integration
Vision Research, 2007 Closed contours are often better perceived than those not fully enclosing an area, i.e., open contours. This facilitation of contour integration by closure, however, has been questioned arguing that in earlier studies closed contours were often "smoother" than open ones, because open contours usually had turning points.
Mathes, Birgit, Fahle, Manfred
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On the complexity of the integral closure [PDF]
Transactions of the American Mathematical Society, 2004 The computation of the integral closure of an affine ring has been the focus of several modern algorithms. We will treat here one related problem: the number of generators the integral closure of an affine ring may require. This number, and the degrees of the generators in the graded case, are major measures of cost of the computation. We prove several
Ulrich, Bernd, Vasconcelos, Wolmer V.
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