Leírás
Abstract: A unital ring $R$ is of module type $(m,n)$ where $m>0$ and $n>m$ are the smallest integers such that $R^m\cong R^n$ if $R$ is not a ring with IBN (invariant basis number). While rings with IBN cover classical rings like rings with chain conditions, free algebras... and it is quite easy to construct rings of module type $(1,2)$, i.e., rings over them all finitely generated free modules are isomorphic, it is a hard job to construct rings of module type $(m, n)$ with $n>2$. In fact, the determination of module type is equivalent to the computation of the Grothendieck group in certain cases, for example for projective-free rings. In this talk we point out how one can use Schreier technique to compute the module type of certain rings via flat bimorphisms putting Leavitt (path) algebras in the frontier of free ideal rings, algebraic K-theory and operator algebras together with some applications.
Zoom link:
https://zoom.us/j/96323581586?pwd=aW9QbGFWcmowTmpPVGFoeFpKYTMyZz09
Meeting ID: 963 2358 1586
Passcode: 897391