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Algebras that are nearly associative

Algebras that are nearly associative
近结合代数
批准号：
153128-2011
负责人：
Bremner, Murray
金额：
$0.8万
依托单位：
University of Saskatchewan
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2012
资助国家：
加拿大
项目状态：
已结题
起止时间：
2012-01-01 至 2013-12-31
来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508426
关键词：
Algebrasnearlyassociative

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英文摘要
The theory of algebraic structures originated in the middle of the 1800's. The field of real numbers had already been extended to include the square root of -1, and this produced the field of complex numbers. Both of these systems satisfy commutativity, ab = ba, and associativity, (ab)c = a(bc). The complex numbers (2-dimensional over the real numbers) were then extended to the quaternions (4-dimensional) which are not commutative. The quaternions were then extended to the octonions (8-dimensional) which are not associative. Properties such as commutativity and associativity are known as polynomial identities for algebras.
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