In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures. These alternate meanings may or may...

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...

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...

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...

one element is zero Lang, Serge (1987), Linear Algebra, Undergraduate Texts in Mathematics, Springer, p. 25, ISBN 9780387964126, We have a zero matrix...

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,...

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...

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...

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...

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...

denote a zero element, which is the identity element for addition (if defined on the structure under consideration) and an absorbing element for multiplication...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

total amount of energy is exactly zero 0 element, or Zero element, one of several generalizations of the number zero to other algebraic structures OE (disambiguation)...

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...

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...

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...

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...

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...

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...

cases, this is the number 0, but it can also refer to a more generalized zero element. In elementary mathematics, the additive inverse is often referred to...