In algebra, the zero object of a given algebraic structure is, in the sense explained below, the simplest object of such structure. As a set it is a singleton...

of vector spaces over a field. See Zero object (algebra) for details. This is the origin of the term "zero object". In Ring, the category of rings with...

is zero Zero (complex analysis), a zero of a holomorphic function Zero element, generalization of the number zero in algebraic structures Zero object (algebra)...

of rings, the zero ring is the terminal object, whereas the ring of integers Z is the initial object. The zero ring, denoted {0} or simply 0, consists...

the trivial non-strict order ≤ . {\displaystyle \,\leq .} Zero object (algebra) – Algebraic structure with only one element List of small groups Rowland...

set of these solutions. Abstract algebra studies algebraic structures, which consist of a set of mathematical objects together with one or several operations...

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

is 0. Thus, every algebraic number field and the field of complex numbers C {\displaystyle \mathbb {C} } are of characteristic zero. The finite field...

algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact sequence of modules (or, more generally, of objects...

"tangible" mathematical objects. A spectral sequence is a powerful tool for this. It has played an enormous role in algebraic topology. Its influence...

universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...

and classification of Lie groups in terms of Lie algebras, which are simpler objects of linear algebra. In more detail: for any Lie group, the multiplication...

category of R-algebras to the category of sets. Free algebras over division rings are free ideal rings. Cofree coalgebra Tensor algebra Free object Noncommutative...

functions on X. The function field of an algebraic variety X (a geometric object defined as the common zeros of polynomial equations) consists of ratios...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class...

Linear algebra is the branch of mathematics concerning linear equations such as: a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

defining quotient objects (also called quotient algebras in universal algebra, and cokernels in category theory). For many types of algebraic structure, the...

manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

The action of a monoid (= commutative ring) R on an object (= ring) A of Ring is an R-algebra. The category of rings has a number of important subcategories...

numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division by zero has no meaning in arithmetic...

is a terminal object in the category of rings. As the initial object is not isomorphic to the terminal object, there is no zero object in the category...

unital associative R-algebra is a monoid object in R-Mod (the monoidal category of R-modules). By definition, a ring is a monoid object in the category of...

K be a field, and L ⊇ K be an algebraically closed extension. An affine algebraic set V is the set of the common zeros in Ln of the elements of an ideal...

initial object in the category of rings. In a similar fashion, if R is any commutative ring, the endomorphisms of an R-module form an algebra over R by...

In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with...

problems and ideas of algebraic number theory and algebraic geometry. The simplest commutative rings are those that admit division by non-zero elements; such...

In abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The...

"abelian category". A category is abelian if it is preadditive and it has a zero object, it has all binary biproducts, it has all kernels and cokernels, and...