# Tag Archives: semisimple

## Semisimple and Jacobson Semisimple

Let $R$ be an associative ring with identity. The Jacobson radical ${\rm Jac}(R)$ of $R$ is the intersection of all the left maximal ideals of $R$. So, ${\rm Jac}(R)$ is a left ideal of $R$. It turns out that the Jacobson radical of $R$ is also the intersection of all the right maximal ideals of […]

## Highlights in Linear Algebraic Groups 12: Radical, Reductive

To analyse the structure of a group G you will need the radical and a torus T. The group of Weyl may also may also suit to prevent the scattering of many a root. Functors are nice including the one of Lie Parabolics bring in the ge-o-metry! The theory of weights may seem oh so […]