All Questions

I was recently studying the Jacobson density theorem and I found it quite interesting. Most textbooks I've seen, including Jacobson's own Basic Algebra, only spend a few lines about the reason why it ...

For a ring $R$ and a group $G$ the group ring $R[G]$ consist of maps from $G$ to $R$ with finite support. It was shown that if the group is fully ordered them this ring can be embedded in a division ...

Suppose $R$ is a strictly ordered (non-commutative) ring, in particular $ab > 0$ for any $a,\, b > 0$, that is also discrete in that there are no elements between $0$ and $1$. Now consider a two-...

Suppose I have a monoid $(M,\, \cdot,\, e)$ equipped with a monoid homomorphism $\textrm{length} : M \rightarrow \mathbb{N}_+$ into the monoid of natural numbers under addition where $e$ is the only ...

Note that throughout rings have a multiplicative identity and are not necessarily commutative Definition: Let $R$ be a ring and let $M\subseteq R$. Then, $M$ is an m-system iff for every $x,y\in ...