Abelian – Definition & Meaning

The term “abelian” is often used in mathematical contexts, but what does it actually mean? In this article, we will explore the definition and meaning of abelian, its origin, associations, synonyms, antonyms, and example sentences.

Definitions

In mathematics, abelian refers to a group or operation that is commutative, meaning that the order in which the elements are multiplied or combined does not affect the result. For example, addition is an abelian operation, while division is not.

Origin

The term abelian comes from the name of the Norwegian mathematician Niels Henrik Abel, who made significant contributions to the study of algebra and number theory in the early 19th century. The term was first used by the German mathematician Ernst Eduard Kummer in 1854.

Meaning in different dictionaries

In the Oxford English Dictionary, abelian is defined as “relating to or denoting a group or operation that is commutative”. The Merriam-Webster Dictionary defines it as “of or relating to an abelian group or ring”. Both definitions emphasize the mathematical usage of the term.

Associations

Abelian is often associated with abstract algebra, which is the study of algebraic structures such as groups, rings, and fields. It is also associated with the work of other prominent mathematicians such as Évariste Galois and Carl Friedrich Gauss.

Synonyms

Some synonyms for abelian include commutative, associative, and symmetric. These terms all describe mathematical operations or structures that have certain properties in common with abelian groups.

Antonyms

Antonyms for abelian include non-commutative, non-associative, and asymmetric. These terms describe operations or structures that do not have the same properties as abelian groups.

The same root words

The root word of abelian is Abel, which comes from the name of the mathematician Niels Henrik Abel. Other words that share this root include Abelian group, Abel’s theorem, and Abel’s identity.

Example Sentences

Here are some example sentences that use the term abelian:

  • “The abelian property of addition makes it easy to solve equations.”
  • “Abelian groups are an important concept in abstract algebra.”
  • “The non-abelian nature of matrix multiplication can make computations more complex.”
  • “Abelian rings have applications in cryptography and coding theory.”

In conclusion, abelian is a term that has a specific meaning in mathematics, referring to groups or operations that are commutative. Its origin lies in the work of the Norwegian mathematician Niels Henrik Abel, and it has associations with abstract algebra and other fields of mathematics. Understanding the meaning of abelian can help us better understand the properties of mathematical structures and operations.

Like this post? Please share to your friends:
Words Wiki
Leave a Reply

;-) :| :x :twisted: :smile: :shock: :sad: :roll: :razz: :oops: :o :mrgreen: :lol: :idea: :grin: :evil: :cry: :cool: :arrow: :???: :?: :!: