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 chain ...

Created with R2024a. Compatible with R2024a and later releases. This curriculum module contains interactive MATLAB® live scripts that teach fundamental matrix methods commonly taught in introductory ...

1 School of Mathematics, Shanghai University of Finance and Economics, Shanghai, China. The category of left -comodule is denoted by. For more about modules and comodules, see [1] -[3] . (a1) is 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 ...

Weak Hopf algebras were introduced by G. Böhm and K. Szlachányi as a generalization of usual Hopf algebras and groupoid algebras [1] [2] . A weak Hopf algebra is a vector space that has both algebra ...

Module theory is also used in investigating bilinear, sesquilinear, and quadratic forms. The authors develop some multilinear algebra (Hom and tensor product) and the theory of semisimple rings and ...

A line drawing of the Internet Archive headquarters building façade. An illustration of a magnifying glass. An illustration of a magnifying glass.

To provide students with an introduction to modern abstract linear algebra. Building on their existing knowledge of matrix methods, students will experience the benefits of the abstract and rigorous ...

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 A ...

A relatively simple, lightweight module of FORTRAN subroutines that perform some common linear algebra procedures. Particularly useful for coding user-defined material models (e.g., plasticity) within ...