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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...

See overview in Oxford Index

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...

See overview in Oxford Index

divisor of zero

Christopher Clapham and James Nicholson.

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

Christopher Clapham and James Nicholson.

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

Christopher Clapham and James Nicholson.

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

Christopher Clapham and James Nicholson.

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

Izzet Coskun and Jason Starr.

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 ℳ0,0(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

Min Ru and Julie Tzu-Yueh Wang.

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

Jian Song.

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

Jan A. Bergstra, Inge Bethke and Alban Ponse.

in The Computer Journal

January 2013; p ublished online March 2012 .

Journal Article. Subjects: Computer Science. 0 words.

Let ℚ0 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

Matthew Baker and Joseph Rabinoff.

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

Gloria Della Noce.

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 DX be a prime...

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

Jack Huizenga.

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

Liansheng Tan and A. C. Pugh.

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 [anull...

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