## “Bulletin Board”

School of Mathematics - August 16, 2008

### Mathematical Lecture

#### Kronecker and Nagata Function Rings and Related (Semi)Star Operations on Integral Domains :A SurveyMarco Fontana Universita' degli Studi "Roma Tre"ItalySeptember 4, 2008

Kronecker and Nagata Function Rings and Related (Semi)Star Operations on Integral Domains :A Survey
Marco Fontana
Universita' degli Studi "Roma Tre"
Italy
September 4, 2008

Abstract

After recalling the motivations that led to the classical constructions of the Kronecker funtion ring and the Nagata ring, in this talk I will present some recent developments related to these constructions, in connection with a new approach to the theory of multiplicative ideal systems in integral domains. In particular, given a Krull's star operation (or a semistar operation, in the sense of Okabe-Matsuda) $\star$ on an integral domain $D$, I will discuss the relations between the multiplicative structure of the ideals in the general constructions of the Nagata ring Na$(D, \star)$ and Kronecker function ring Kr$(D, \star)$ and I will present some results obtained recently in a joint work with Alan Loper (Ohio State University).

Information:

 Date: Thursday, September 4, 2008, 10:00-12:00 Place: Niavaran Bldg., Niavaran Square, Tehran, Iran