Hebrew University Amitsur Algebra Seminar ---------------------------------- Time: Thursday, March 22, 12:00-13:15 Place: math 209 Speaker: Uriya First Title: Rings of Invariants Abstract: Classical invariant theory studies subrings composed of elements which are fixed by a group action on the ambient ring. Generalizing this setup, we call a subring of a ring R "invariant" if it is the set of elements fixed by an arbitrary set of endomorphisms of R, and "semi-invariant" if it is the set of elements fixed by a set of endomorphisms of some ring containing R. Centralizers are but one of the important examples for semi-invariant subrings. The main question from a ring-theoretic point of view is what properties of R pass to invariant or semi-invariant subrings. We will show that important variations of semi-locality is inherited by semi-invariant subrings: if R is semiprimary (resp.: left/right perfect, semiperfect and $\pi$-regular, $\pi$-regular), then so is any semi-invariant subring of R. In addition, if R is semilocal complete, then any invariant subring of $R$ is semilocal complete. To round things up, we will show that being Artinian or semiperfect does not pass to invariant subrings. As an application, we will discuss the existence of "Jordan forms" for automorphism of modules with semiperfect and $\pi$-regular endomorphism ring. All ring theoretic notions will be defined during the talk. You are cordially invited! <http://math.huji.ac.il/amitsur.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Gili Schul <gili.schul@mail.huji.ac.il>