Speaker: Jay Shapiro, George Mason University

Title: The transfer of properties from a ring to the fixed ring.

Abstract: Let $G$ be a group acting via ring automorphisms on a commutative unital ring $R$. We examine the properties of $R$ that are inherited by the fixed ring $R^G = \{a\in R: g(a) =a$ for all $g\in G\}$ under varying assumptions on $R$ and $G$. This question has it roots in Galois Theory and Hilbert's 14th Problem. With certain finiteness conditions on G, there is a close relation between $R$ and $R^G$. However, without these conditions, the fixed ring can often behave badly as we show with examples. Nonetheless with some different assumptions, certain properties do transfer between the rings.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491