Vladimir Kirichenko
Kiev National University, Ukraine
Quivers of associative rings.
Abstract: The notion of a quiver for a finite dimensional algebra over an algebraically closed field was introduced by P.Gabriel in 1972 in connection with problems of the representation theory of finite dimensional algebras. We consider different definitions of a quiver for a semiperfect and associative ring. We study the properties of rings using the properties of their quivers. For example, a Noetherian semiperfect ring $A$ is serial if and only if its right quiver $Q(A)$ and left quiver $Q^{\prime} (A)$ are disconnected unions of simple cycles and oriented chains.