Homological algebra and module theory constitute a vibrant area of contemporary mathematics, interweaving concepts from algebra, topology and geometry. At its core, homological algebra studies ...

This module is designed to bridge the theoretical knowledge from matrix algebra with practical computational applications. You will learn to interpret and utilize matrix operations, solve systems of ...

You saw an example of the first type, in the mixing example. Eigenvalue problems come up in a number of engineering and science applications. You will cover the application of eigenvalues in the last ...

Abstract In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A ...

Algebra and calculus are essential branches of mathematics and for most students are the main areas of maths they have seen at high school. Algebra involves manipulating expressions and solving ...

Assume that is a Hopf algebra with antipode, a left Yetter-Drinfeld module over is a -vector space which is both a left -module and left -comodule and satisfies the compatibility condition for all.

Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra, as well as papers of related areas which have applications to algebra.

Before you start, it may be helpful to read the guides on coordinates and graphs from Module 2 (M2) and Module 3 (M3). When two lines are perpendicular, the product of their gradients is 1. Lines ...

Before reading this guide, it may be helpful to read the guide from Module 7 (M7) about proportion and variation. Module 7 (M7) proportion and variation is concerned with direct proportion between ...

In this paper a symbolic analysis of the equations that allow to calculate the values of the series and parallel resistances appearing in the single diode model of a photovoltaic module is presented.