# zero divisor

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## zero divisor

[¦zir·ō di′vīz·ər]
(mathematics)
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An element x [member of] NQR is called a zero divisor if there exists a nonzero element y [member of] NQR such that xy = 0.
For the coordinate function (1) we can define the deferential zero divisor,
In this picture distinct statistics follows from the existence of the two types of "light-cones" in the octonionic (4+4)-space (9), what shows itself in the definitions of the primitive zero divisors (26) and (30).
2] is a zero divisor, so there exists a nonzero ([a.
If S is antinegative and has no zero divisors then [S.
Coverage includes a guide to closure operations in commutative algebra, a survey of test ideals, finite-dimensional vector spaces with Frobenius action, finiteness and homological conditions in commutative group rings, regular pullbacks, noetherian rings without finite normalization, Krull dimension of polynomial and power series rings, the projective line over the integers, on zero divisor graphs, and a closer look at non-unique factorization via atomic decay and strong atoms.
Lee, Power series rings satisfying a zero divisor porperty, Comm.
4 is either the ring without zero divisors or the ring with [R.
An element a [member of] R\{0} is a S-weak zero divisor if there exists b [member of] R\{0, a} such that a, b = 0 satisfying the following conditions: There exists x, y [member of] R\{0, a, b} such that
Left zero divisors are right zero divisors, if ab = 0 implies ba = 0.
Let N be a weak commutative near-ring without non-zero zero divisors.

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