Zero element information

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...

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...

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...

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

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

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)...

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...

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...

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...

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...

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...

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...

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...

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. If q = pk, all...

1932 discovery of the neutron) for the hypothetical "element of atomic number zero" (with zero protons in its nucleus) that he placed at the head of...

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...

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...