How Do You Spell ABELIAN?

Pronunciation: [ˈe͡ɪbə͡lˌi͡ən] (IPA)

The word "Abelian" is pronounced as /əˈbiːliən/ in the IPA phonetic transcription. This word refers to a mathematical concept related to groups, which were named after the Norwegian mathematician Niels Henrik Abel. The spelling of "Abelian" includes the letter "a" before "b" because it is derived from the name "Abel". This letter "a" changes the pronunciation of the first syllable to /ə/ instead of /eɪ/, which would be expected if it were spelled as "Ebelian".

ABELIAN Meaning and Definition

1. Abelian is an adjective used in mathematics to describe a group, set, or algebraic structure in which a certain mathematical operation, such as addition or multiplication, follows a specific property known as commutativity. A group or set is said to be Abelian if the order of the elements does not affect the result of the operation. In other words, if the operation is denoted by a symbol like "+", then for any two elements "a" and "b" in an Abelian set, the order of their addition does not matter, and "a + b" will always yield the same result as "b + a".

   The term "Abelian" is derived from the name of a 19th-century Norwegian mathematician, Niels Henrik Abel, who made significant contributions to the theory of equations and algebraic functions. Although Abel's work was broader than the concept of Abelian groups, his name became associated with these structures due to his foundational work in the theory.

   Abelian groups are particularly important in abstract algebra, as they serve as a fundamental building block for more complex structures and mathematical theories. They find applications in various areas of mathematics, including number theory, algebraic geometry, and representation theory. The study of Abelian groups and their properties has led to deep insights into the structure and behavior of mathematical objects and has paved the way for the development of broader algebraic theories.

Common Misspellings for ABELIAN

• abalan
• abelia
• beldan
• zbelian
• sbelian
• wbelian
• qbelian
• avelian
• ahelian
• agelian
• abwlian
• abslian
• abdlian
• abrlian
• ab4lian
• ab3lian
• abekian
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• abeluan
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• attellan
• Beliah
• tabelion
• abilin
• aeliaa
• ablians
• aabelians
• Dadelian
• Asetian
• Aielian
• Sabilian
• Sabelien
• Abuliah
• Fabylian
• Subeliac
• Napelian
• Ablaian
• Fabbelia
• Brelian
• cabelmin
• cabelman
• Abeliae
• Abyilah
• Abslan
• beplian

Etymology of ABELIAN

The word "Abelian" is derived from the name of the Norwegian mathematician Niels Henrik Abel. Abel made significant contributions to the field of mathematics, particularly in the study of algebra and the theory of equations. The term "Abelian" is used to describe mathematical structures or properties that are related to or follow the ideas and principles pioneered by Abel. Specifically, in the field of algebra, it refers to commutative groups, rings, or other structures where the operation is commutative, meaning the order of operations does not matter.