Abelian example sentences

"Abelian" Example Sentences

1. Group theory is the study of abelian and non-abelian groups.
2. An abelian group is a group in which the order of the elements does not matter.
3. The integers under addition form an abelian group.
4. The non-zero rational numbers under multiplication form an abelian group.
5. The multiplication of matrices is not always abelian.
6. Every subgroup of an abelian group is abelian.
7. The direct sum of two abelian groups is abelian.
8. The commutative property is also called the abelian property.
9. An abelian variety is a projective algebraic variety that is also an abelian group.
10. Abelian cohomology is the study of cohomology groups of abelian groups.
11. The automorphism group of an abelian group is a special subgroup of the general linear group.
12. The Pontryagin duality theorem is a fundamental result in the theory of abelian groups.
13. The abelian sandpile model is a mathematical model used in physics to study self-organized criticality.
14. An abelian extension of a field F is a Galois extension whose Galois group is abelian.
15. The abelian Higgs model is a theoretical model used in high energy physics to explain the spontaneous breaking of symmetry.
16. Abelian varieties were first introduced by the mathematician Carl Jacobi in the mid-19th century.
17. The classification of finite abelian groups is a fundamental part of group theory.
18. An abelian Lie group is a Lie group in which the group operation is commutative.
19. The abelian sandpile model is an example of a cellular automaton.
20. The Euler characteristic of an abelian group is given by the alternating sum of the orders of the group elements.
21. The cohomology of an abelian scheme is closely related to the arithmetic geometry of the underlying scheme.
22. An abelian category is a category in which every morphism has a kernel and a cokernel.
23. The abelian group structure of the Jacobian variety of an algebraic curve is a fundamental object in algebraic geometry.
24. The study of abelian subgroups of algebraic groups is a central topic in the theory of algebraic groups.
25. An abelian integral is a function that can be expressed as an integral of rational functions in a given algebraic function.
26. An abelian cover is a cover of a space in which the fundamental group of the covering space is abelian.
27. The abelian sandpile model exhibits a variety of interesting phenomena, including criticality, avalanches, and power laws.
28. An abelian Galois extension is a Galois extension whose Galois group is abelian.
29. The Tate conjecture is a famous open problem in algebraic geometry that concerns the Hodge and étale cohomology of abelian varieties.
30. The abelian sandpile model is closely related to various other models in physics and mathematics, including the Ising model and percolation.

Common Phases

1. Abelian group;
2. Abelian variety;
3. Abelian theorem;
4. Abelian Lie algebra;
5. Abelian category;
6. Abelian sheaf;
7. Abelian sandpile model;
8. Abelian Higgs model;
9. Abelian bosonization;
10. Abelian dominance.