Algorithms for Extending Gröbner Bases
to Subalgebras and Their Ideals
Date: July 19th (Friday)
Time: 08:30-09:00
Abstract
This talk summarizes the results of my 1994 doctoral dissertation,
in which methods were presented
for generalizing the theory of Gröbner bases
to four distinct contexts:
First, we outline the results
developed by Robbiano and Sweedler in 1987
and by Sweedler in 1988 to extend
Gröbner basis theory in an intrinsic manner to k-subalgebras of a
polynomial ring k[x1,...,xn]
over a field k
and to their ideals.
We will present additional results that enable us
actually to compute SAGBI-Gröbner bases
(analogs to Gröbner bases for ideals of k-subalgebras) in
k[x1,...,xn]
and also to use them in applications.
Then, we will extend SAGBI and SAGBI-Gröbner theory to the more
general
context of a polynomial ring over a noetherian integral domain,
describing algorithms for computing
these bases and offering some
applications.
