Examples of 'abelian groups' in a sentence
Meaning of "abelian groups"
in mathematics, refers to a type of mathematical structure consisting of a set together with an operation that is commutative, meaning the order of the elements does not affect the outcome of the operation
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- plural of abelian group
How to use "abelian groups" in a sentence
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abelian groups
These are both sheaves of abelian groups.
Abelian groups generalize the arithmetic of addition of integers.
Structure theorem for finite abelian groups.
The finitely generated abelian groups can be completely classified.
Probability distributions on locally compact abelian groups.
The structure of finitely generated abelian groups in particular is easily described.
This follows from the classification of finitely generated abelian groups.
Fundamental theorem of abelian groups it explains.
This is a key step in the classification of finitely generated abelian groups.
Fundamental theorem of abelian groups explain.
The category of abelian groups forms a full subcategory of the category of groups.
Mean value on locally compact abelian groups.
Constant sheaves of abelian groups appear in particular as coefficients in sheaf cohomology.
Classification of finitely generated abelian groups.
The direct sum of abelian groups is a prototypical example of a direct sum.
See also
Tensor product of abelian groups.
Finitely generated abelian groups are completely classified and are particularly easy to work with.
Suppose we have the following short exact sequence of abelian groups.
Both are abelian groups.
The conjecture has been proved for finitely generated abelian groups.
So let be abelian groups.
The new combinatorial topology formally treated topological classes as abelian groups.
Category of abelian groups.
The theorem also holds more generally in locally compact abelian groups.
The finite simple abelian groups are exactly the cyclic groups of prime order.
Characterization of abelian groups.
Free abelian groups have properties which make them similar to vector spaces.
Classification of abelian groups.
In all abelian groups every conjugacy class is a set containing one element singleton set.
This information is usually contained in a rank three lattice of abelian groups or modules.
He solved the problem of finding which abelian groups have a finite number of indecomposable modules.
Therefore the free product is not the coproduct in the category of abelian groups.
A commutative monoid in the category of simplicial abelian groups is a simplicial commutative ring.
This construction makes simplicial homology a functor from simplicial complexes to abelian groups.
The projective objects in the category of abelian groups are the free abelian groups.
The term rank has a different meaning in the context of elementary abelian groups.
For abelian groups all automorphisms except the trivial one are called outer automorphisms.
The same is true for the rank of abelian groups and the length of modules.
This implies that all the sets involved in the sequence are in fact abelian groups.
Consider the category Ab of abelian groups and group homomorphisms.
The rank problem is decidable for finite groups and for finitely generated abelian groups.
The representation theory for locally compact abelian groups is described by Pontryagin duality.
Basic algebraic structures with such an addition operation include commutative monoids and abelian groups.
He worked especially in the theory of Abelian groups and ring theory.
All abelian groups are Dedekind groups.
Probability distribution on locally compact Abelian groups.
Let Abt be the category of abelian groups with torsion and also the zero group.
The original example of an additive category is the category Ab of abelian groups.
Ab, abelian groups and group homomorphisms.
Consider the category D of homomorphisms of abelian groups.
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Every finite abelian group is a torsion group
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