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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=545603
• 关键词: Algebras; nearly; associative

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.

代数结构理论起源于19世纪中期。实数领域已经扩展到包括-1的平方根，这就产生了复数领域。这两个系统都满足交换性ab = ba和结合性ab)c = a（bc）。然后将复数（实数上的二维）扩展到不可交换的四元数（四维）。然后将四元数扩展到不结合的八元数（8维）。交换性和结合性等性质被称为代数的多项式恒等式。