Research in universal algebra

普适代数研究

• 批准号: 121349-2008
• 负责人: Willard, Ross
• 金额: $ 1.6万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=475495
• 关键词: Research; universal; algebra

Ordinary algebra studies the laws of addition, subtraction, multiplication and division of ordinary numbers. Branches of modern algebra study certain "nonstandard" systems of algebra which arise in various contexts. A simple example is Boolean algebra, which is the system of laws modeled by the boolean operators AND, OR, XOR, and NOT as they act on the two boolean truth values 0 ("false") and 1 ("true"). Much more complicated systems of algebra, most of them bizarre, some of them useful in physics, chemistry, theoretical computer science and engineering, can be invented, studied, and modeled. Universal algebra is the general study of patterns in, and the limits of, nonstandard laws of algebra and their models.

普通代数研究普通数字的加法、减法、乘法和除法的规律。现代代数的分支研究在各种情况下出现的某些“非标准”代数系统。一个简单的例子是布尔代数，它是由布尔运算符AND、OR、XOR和NOT建模的定律系统，因为它们作用于两个布尔真值0（“假”）和1（“真”）。更复杂的代数系统，其中大多数是奇怪的，其中一些在物理，化学，理论计算机科学和工程中很有用，可以被发明，研究和建模。通用代数是对非标准代数定律及其模型的模式和极限的一般研究。