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...

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

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...

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...

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...

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,...

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...

of an element x, denoted −x, is the element that when added to x, yields the additive identity. This additive identity is often the number 0 (zero), but...

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...

Neutronium (or neutrium, neutrite, or element zero) is a hypothetical substance made purely of neutrons. The word was coined by scientist Andreas von Antropoff...

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...

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...

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...

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 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...

same element), a ring with one element must be the zero ring, which does not behave like a finite field. For instance, all modules over the zero ring...

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...

In mathematics, an element z {\displaystyle z} of a Banach algebra A {\displaystyle A} is called a topological divisor of zero if there exists a sequence...

two-player, zero-sum game can be found by solving a linear programming problem. Suppose a zero-sum game has a payoff matrix M where element Mi,j is the...

x_{k}} and zero at every x j , j ≠ k {\displaystyle x_{j},\;j\neq k} . Depending on the author, the word "element" in the "finite element method" refers...

quadratic form q, written (X, q), a null vector or isotropic vector is a non-zero element x of X for which q(x) = 0. In the theory of real bilinear forms, definite...

aligned with the practice in algebra of denoting the exclusion of the zero element with a star, and should be understandable to most practicing mathematicians...

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...

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...

significant advantage in that each new zero element a i j {\displaystyle a_{ij}} affects only the row with the element to be zeroed (i) and a row above (j). This...

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...

M {\displaystyle 0_{M}} is the zero element of M {\displaystyle M} and 0 R {\displaystyle 0_{R}} is the zero element of R {\displaystyle R} ). A free...

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