Look up Abelian or abelian in Wiktionary, the free dictionary. Abelian may refer to: Abelian group, a group in which the binary operation is commutative...

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements...

Look up abelian or Abelian in Wiktionary, the free dictionary. Non-abelian or nonabelian may refer to: Non-abelian group, in mathematics, a group that...

The motivating prototypical example of an abelian category is the category of abelian groups, Ab. Abelian categories are very stable categories; for...

in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group...

In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is...

pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more detail, this means that a category C is pre-abelian if:...

In mathematics, an abelian surface is a 2-dimensional abelian variety. One-dimensional complex tori are just elliptic curves and are all algebraic, but...

Abelians (Latin: Abelonii; also Abelites, Abeloites or Abelonians) were a Christian sect that emerged in the 4th century in the countryside near Hippo...

In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists...

is abelian. Equivalently, a group G is metabelian if and only if there is an abelian normal subgroup A such that the quotient group G/A is abelian. Subgroups...

In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which...

In abstract algebra, an abelian group ( G , + ) {\displaystyle (G,+)} is called finitely generated if there exist finitely many elements x 1 , … , x s...

Hovhannes Harutyuni Abelian (Armenian: Հովհաննես Աբելյան, October 23, 1865, Shamakhi, Baku Governorate, Russian Empire - July 1, 1936, Yerevan, Soviet...

In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named...

In mathematics, a topological abelian group, or TAG, is a topological group that is also an abelian group. That is, a TAG is both a group and a topological...

of abelian group, since the abelian groups are exactly the modules over the ring of integers. Like a vector space, a module is an additive abelian group...

In mathematics, a free abelian group is an abelian group with a basis. Being an abelian group means that it is a set with an addition operation that is...

group is non-commutative, then the gauge theory is referred to as non-abelian gauge theory, the usual example being the Yang–Mills theory. Many powerful...

becomes a Lie algebra. Such a Lie algebra is called abelian. Every one-dimensional Lie algebra is abelian, by the alternating property of the Lie bracket...

fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to...

solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose...

differentials. In either case the definition has its origins in the theory of abelian integrals. The dimension of the space of differentials of the first kind...

In mathematics, the endomorphisms of an abelian group X form a ring. This ring is called the endomorphism ring of X, denoted by End(X); the set of all...

following groups are virtually abelian. Any abelian group. Any semidirect product N ⋊ H {\displaystyle N\rtimes H} where N is abelian and H is finite. (For example...

In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same...

In mathematics, specifically in category theory, a quasi-abelian category is a pre-abelian category in which the pushout of a kernel along arbitrary morphisms...

an innovator in the field of elliptic functions and the discoverer of Abelian functions. He made his discoveries while living in poverty and died at...

In functional analysis, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute. The prototypical...

breaking. A similar problem arises with Yang–Mills theory (also known as non-abelian gauge theory), which predicts massless spin-1 gauge bosons. Massless weakly-interacting...