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...

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...

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...

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...

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...

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

semigroup with one element, then the Cayley table of S is The only element in S is the zero element 0 of S and is also the identity element 1 of S. However...

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...

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...

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...

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,...

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...

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...

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...

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...

the additive inverse of an element x, denoted −x, is the element that when added to x, yields the additive identity, 0 (zero). In the most familiar cases...

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...

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...

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...

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...

from R to S. If 0S is the zero element of S, then the kernel of f is its kernel as additive groups. It is the preimage of the zero ideal {0S}, which is, the...

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...

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...

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...

characteristic 2 then every element has a unique square root. In a field of any other characteristic, any non-zero element either has two square roots...

except by zero, is always possible. Formally, we start with a non-zero algebra D over a field. We call D a division algebra if for any element a in D and...

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...

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...