This field examines the interplay between algebraic systems—such as groups, rings, fields and modules—and the powerful analytical framework provided by local-global principles. These principles offer ...

Abstract: Among probabilistic graphical models, the class of algebraic Bayesian networks stands out. The theory of algebraic Bayesian networks is based on the decomposition of knowledge into knowledge ...

“THIS volume is the first part of a work designed it provide a convenient account of the foundations and methods of modem algebraic geometry.” These words from the authors' preface explain the scope ...

Before taking a look at simplifying algebraic fractions, let's remind ourselves how to simplify numerical fractions. Sometimes the top and bottom of a fraction can be divided by the same number. This ...

The existence of an algebraic closure can be proven using ultraproducts. This is quite interesting as an example of the application of model theory. A Proof of The Existence of An Algebraic Closure ...

Adding and subtracting algebraic fractions is a similar process to adding and subtracting normal fractions. The denominators of each fraction are different, \(3t\) and \(7t\), so a common denominator ...

在 :numref:`proving_identities_in_algebraic_structures` 中，我们看到许多关于实数的常见恒等式适用于更一般的代数结构类，比如交换环 ...

An algebraic distance graph is defined to be a graph with vertices in E n in which two vertices are adjacent if and only if the distance between them is an algebraic number. It is proved that an ...