Some applications of transfinite numbers to algebra and some applications of number theory to transfinite numbers
Abstract.
In the first part we will survey the role of transfinite numbers in the study of Hilbert’s basis theorem and its extension by MacLagan. To this end we associate ordinals to some natural well partial orderings related Cartesian products of the set of natural numbers and we apply this apparatus to monomial ideals in F[X_1,…,X_n] where F is a field.
In the second part we use the machinery of Tauberian theorems to prove some structural results about transfinite numbers regarding limit laws and phase transitions.
The talk will be non technical and it is aimed at a general mathematical audience.
The seminar will be held via Zoom and everyone can join via the link:
https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09
Topic: Онлайн семинар на секция “Алгебра и логика”
Time: Mar 19, 2021 04:00 PM Sofia
Meeting ID: 851 3737 5021
Passcode: 035647
Algebra and Logic Department, IMI-BAS
http://www.math.bas.bg/algebra/seminarAiL/