All Questions

Let $A$ be a Baer $*$-ring. Let us denote $B$ by the space of all upper triangular matrices $\left(\begin{array}{cc} a_1& a_2 \\ 0 & a_4 \end{array}\right)$ where $a_i$'s are in $A$. Is $B$ ...

Let $G$ be a countable discrete group (not necessarily abelian), and suppose the group ring $\mathbb{Z}G$ is a left-Noetherian ring, for example, when $G$ is a polycyclic-by-finite group. Denote the ...

What are the simplest examples of rings that are not isomorphic to their opposite rings? Is there a science to constructing them? The only simple example known to me: In Jacobson's Basic Algebra (...