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divisor of zero

Overview page. Subjects: Mathematics.

If in a ring there are non-zero elements *a* and *b* such that *ab*=0, then *a* and *b* are divisors of zero. For example, in the ring of 2×2 real matrices,

and so each of the matrices on...

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divisor of zero

Overview page. Subjects: Mathematics.

If in a ring there are non-zero elements *a* and *b* such that *ab*=0, then *a* and *b* are divisors of zero. For example, in the ring of 2×2 real matrices,

and so each of the matrices on...

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divisor of zero

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 100 words.

If in a *ring there are non-zero elements *a* and *b* such that *ab*=0, then *a* and *b*

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divisor of zero

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 82 words.

If in a *ring there are non‐zero elements *a* and *b* such that *ab*=0, then *a* and *b...*

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greatest common factor

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 203 words.

For two non‐zero integers *a* and *b*, any integer that is a divisor of both is a *common divisor...

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greatest common factor

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 198 words.

For two non-zero integers *a* and *b*, any integer that is a divisor of both is a *common

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zero divisors

Overview page. Subjects: Mathematics.

Non-zero elements in a ring whose product is zero. There are no zero divisors within the real or complex numbers, but there are in other systems. For example, if and then so **A** and **B** are...

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Divisors on the space of maps to Grassmannians

in** International Mathematics Research Notices**

January 2006; p ublished online January 2006 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

We study the divisor theory of the Kontsevich moduli spaces ℳ_{0,0}(*G*(*k,n*),*d*) of genus-zero stable maps to the Grassmannians. We calculate the classes of several geometrically significant...

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An Effective Schmidt’s Subspace Theorem for Projective Varieties Over Function Fields

in** International Mathematics Research Notices**

January 2012; p ublished online March 2012 .

Journal Article. Subjects: Mathematics. 5888 words.

We deduce an effective version of Schmidt’s subspace theorem on a smooth projective variety over a function field of characteristic zero for divisors of coming from hypersurfaces in .

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greatest common factor

Overview page. Subjects: Mathematics.

For two non-zero integers *a* and *b*, any integer that is a divisor of both is a common divisor. Of all the common divisors, the greatest is the greatest common divisor (or g.c.d.), denoted by...

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Some Type I Solutions of Ricci Flow with Rotational Symmetry

in** International Mathematics Research Notices**

January 2015; p ublished online October 2014 .

Journal Article. Subjects: Mathematics. 5483 words.

We prove that the Ricci flow on [math] blown-up at one point starting with any rotationally symmetric Kähler metric must develop Type I singularities. In particular, if the total volume...

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Cancellation Meadows: A Generic Basis Theorem and Some Applications<sup>†</sup>

in** The Computer Journal**

January 2013; p ublished online March 2012 .

Journal Article. Subjects: Computer Science. 0 words.

Let ℚ_{0} denote the rational numbers expanded to a ‘meadow’, that is, after taking its zero-totalized form (0^{−1}=0) as the preferred interpretation. In this paper, we consider ‘cancellation...

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The Skeleton of the Jacobian, the Jacobian of the Skeleton, and Lifting Meromorphic Functions From Tropical to Algebraic Curves

in** International Mathematics Research Notices**

January 2015; p ublished online October 2014 .

Journal Article. Subjects: Mathematics. 13234 words.

Let [math] be an algebraically closed field which is complete with respect to a nontrivial, non-Archimedean valuation and let [math] be its value group. Given a smooth, proper, connected...

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On the Picard Number of Singular Fano Varieties

in** International Mathematics Research Notices**

January 2014; p ublished online November 2012 .

Journal Article. Subjects: Mathematics. 9140 words.

Let *X* be a -factorial Gorenstein Fano variety. Suppose that the singularities of *X* are canonical and that the locus where they are nonterminal has dimension zero. Let *D*⊂*X* be a prime...

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Restrictions of Steiner Bundles and Divisors on the Hilbert Scheme of Points in the Plane

in** International Mathematics Research Notices**

January 2013; p ublished online August 2012 .

Journal Article. Subjects: Mathematics. 10297 words.

The Hilbert scheme of *n* points in the projective plane parameterizes degree *n* zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving...

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A novel method to determine the finite and infinite frequency structure of a rational matrix

in** IMA Journal of Mathematical Control and Information**

June 2001; p ublished online June 2001 .

Journal Article. Subjects: Mathematics. 0 words.

A novel method is proposed for determining the finite and infinite frequency structure of any rational matrix. For a polynomial matrix, a natural relationship between the rank information of...

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integral domain

Overview page. Subjects: Mathematics.

A commutative ring *R* with identity, with the additional property that

**9.** For all *a* and *b* in *R*, *ab*=0 only if *a*=0 or *b*=0.(The axiom numbering follows on from that used...

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residue class

Overview page. Subjects: Mathematics.

(modulo n)

An equivalence class for the equivalence relation of congruence modulo *n*. So, two integers are in the same class if they have the same remainder upon division by *n*. If [*a*null...