In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures. These alternate meanings may or may...
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In abstract algebra, an element a of a ring R is called a left zero divisor if there exists a nonzero x in R such that ax = 0, or equivalently if the...
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Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in...
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usually required to be at least distinct from zero, and often distant from it; in this case finding this element is called pivoting. Pivoting may be followed...
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one element is zero Lang, Serge (1987), Linear Algebra, Undergraduate Texts in Mathematics, Springer, p. 25, ISBN 9780387964126, We have a zero matrix...
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element of the domain of a function, where the value of the function is zero Zero (complex analysis), a zero of a holomorphic function Zero element,...
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absorbing element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because...
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List of roller coaster elements (redirect from Corkscrew (roller coaster element))
hill. The element gets its name from the weightless effect of zero g-force that a rider experiences during the inversion. A zero-g stall or zero-gravity...
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0 (redirect from Zero function)
denote a zero element, which is the identity element for addition (if defined on the structure under consideration) and an absorbing element for multiplication...
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Torsion (algebra) (redirect from Torsion element)
specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion...
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In algebra, an irreducible element of an integral domain is a non-zero element that is not invertible (that is, is not a unit), and is not the product...
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with zero morphisms. If C is a preadditive category, then every hom-set Hom(X,Y) is an abelian group and therefore has a zero element. These zero elements...
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neutral element (the zero vector in the case of vector spaces, the identity element in the case of commutative groups, and the zero element in the case...
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primitive (q − 1)th root of unity in GF(q); this means that each non-zero element of GF(q) can be written as αi for some natural number i. If q is a prime...
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Discrete valuation ring (redirect from Uniformizing element)
principal ideal domain with a unique non-zero prime ideal. R is a principal ideal domain with a unique irreducible element (up to multiplication by units). R...
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module is a module over a ring such that zero is the only element annihilated by a regular element (non zero-divisor) of the ring. In other words, a module...
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Planet Funk In mathematics, a non-zero element is any element of an algebraic structure other than the zero element. Nonzero: The Logic of Human Destiny...
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Null semigroup (redirect from Zero semigroup)
called a zero semigroup) is a semigroup with an absorbing element, called zero, in which the product of any two elements is zero. If every element of a semigroup...
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the "empty sum is zero" extension is standard practice in mathematics and computer programming (assuming the domain has a zero element). For the same reason...
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mathematics, the zero ring or trivial ring is the unique ring (up to isomorphism) consisting of one element. (Less commonly, the term "zero ring" is used...
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non-zero element of this field is called a quadratic residue if it is a square in Z/pZ, and otherwise, it is called a quadratic non-residue. Zero, while...
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Rng (algebra) (redirect from Adjoining an identity element)
every position where a sequence in the subset has a non-zero element at that position, and zero in every other position. Ideals, quotient rings, and modules...
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Initial and terminal objects (redirect from Terminal element)
Set, the category of sets. Every one-element set (singleton) is a terminal object in this category; there are no zero objects. Similarly, the empty space...
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group structure is usually identified as addition, and the only element is called zero, so the object itself is typically denoted as {0}. One often refers...
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case of a field F, the group is (F ∖ {0}, •), where 0 refers to the zero element of F and the binary operation • is the field multiplication, the algebraic...
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but not the same in general. An element p of a commutative ring R is said to be prime if it is not the zero element or a unit and whenever p divides...
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positive integer). In a field of order pk, adding p copies of any element always results in zero; that is, the characteristic of the field is p. For q = pk,...
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non-zero and have no non-zero proper submodules. Equivalently, a module M is simple if and only if every cyclic submodule generated by a non-zero element...
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square n × n matrix A such that its element Aij is one when there is an edge from vertex ui to vertex uj, and zero when there is no edge. The diagonal...
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