An online session of the Algebra and Logic Seminar will be held on **January 7, 2022** (Friday) **at 1:00 pm (UTC+2). **A talk on

**A valuation theorem for Noetherian rings**

**A valuation theorem for Noetherian rings**

will be delivered by **Antoni Rangachev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences)**.

**Abstract. **A classical result due to Krull says that a normal domain R is equal to the intersection of the valuation rings in its field of fractions that contain R. If in addition R is Noetherian, then one can restrict the intersection to the discrete valuation rings that contain R. Now consider the following relative setting. Let A and B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra that contains A. Denote by A’ the integral closure of A in B. In this talk I will show that A’ is determined by finitely many unique discrete valuation rings. This result generalizes Rees’ classical valuation theorem for ideals. If time permits I will obtain a variant of Zariski’s main theorem.

The seminar will be held via Zoom and everyone can join at:

https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09

Topic: Онлайн семинар на секция “Алгебра и логика”

Time: Jan 07, 2022 01:00 PM Sofia

Meeting ID: 851 3737 5021

Passcode: 035647

Algebra and Logic Department, IMI-BAS

http://www.math.bas.bg/algebra/seminarAiL/

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