CYCLOTOMY Meaning and
Definition
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Cyclotomy is a mathematical concept that deals with the study of cyclotomic fields. It is a branch of number theory that focuses on the properties and characteristics of these fields, which are extensions of the field of rational numbers obtained by adjoining roots of unity.
In cyclotomy, the term 'cyclotomic field' refers to a field that is generated by adjoining a primitive root of unity to the field of rational numbers. An important aspect of cyclotomy is the study of cyclotomic polynomials, which are polynomials that have as their roots the primitive nth roots of unity. These polynomials play a crucial role in the construction and analysis of cyclotomic fields.
Cyclotomy involves investigating various properties of cyclotomic fields, such as their Galois groups, their roots of unity, and their relationship with other algebraic structures. It explores topics like the factorization of cyclotomic polynomials, the structure of the units in cyclotomic fields, and the behavior of cyclotomic fields under certain arithmetic operations.
The study of cyclotomy has important applications in many areas of mathematics, including algebraic number theory, algebraic geometry, and cryptography. It provides insights into the structure of certain number fields and helps in understanding the properties of their elements. Cyclotomy also has connections with other branches of mathematics, such as the theory of modular forms and elliptic curves.
Overall, cyclotomy is a mathematical discipline that investigates the properties and structures of cyclotomic fields, playing a significant role in number theory and its various applications.
Common Misspellings for CYCLOTOMY
- cylotomy
- xyclotomy
- vyclotomy
- fyclotomy
- dyclotomy
- ctclotomy
- cgclotomy
- chclotomy
- cuclotomy
- c7clotomy
- c6clotomy
- cyxlotomy
- cyvlotomy
- cyflotomy
- cydlotomy
- cyckotomy
- cycpotomy
- cycootomy
- cyclitomy
- cyclktomy
Etymology of CYCLOTOMY
The word "cyclotomy" is derived from the Greek roots "kyklos", meaning "circle" or "cycle", and "tomos", meaning "cutting" or "division". Therefore, the etymology of "cyclotomy" can be understood as "the cutting or division of circles or cycles". In mathematics, "cyclotomy" refers to the study of division of the circumference of a circle into a certain number of equal arcs, particularly in relation to constructing regular polygons with a compass and straightedge.
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