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: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=522524
• 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.

代数结构的理论起源于1800年代中期。 实际数字的字段已经扩展到包括-1的平方根，这产生了复数的字段。 这两个系统都满足了换向性，AB = BA和关联性，（AB）C = A（BC）。 然后将复数（对实数上的二维）扩展到不合理的四季度（4维）。 然后将四元组扩展到非关联的八元（8维）。 诸如通勤和关联之类的特性称为代数的多项式身份。