Hebrew University
Amitsur Algebra Seminar
Time: Thursday, March 22, 12:00-13:15
Place: math 209
Speaker: Uriya First
Title: Rings of Invariants
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!
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Gili Schul   <gili.schul@mail.huji.ac.il>