Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584276 | Journal of Algebra | 2015 | 15 Pages |
Abstract
Let R be an integral domain over a field k, and G a subgroup of the automorphism group of the polynomial ring R[x1,â¦,xn] over R. In this paper, we discuss when G is diagonalizable under the assumption that G is diagonalizable over the field of fractions of R. We are particularly interested in the case where G is a finite abelian group. Kraft and Russell (2014) [8] imply that every finite abelian subgroup of AutRR[x1,x2] is diagonalizable if R is an affine PID over k=C. One of the main results of this paper says that the same holds for a PID R over any field k containing enough roots of unity.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Shigeru Kuroda,