Abstract
In this paper we study algebraic sets of pairs of matrices defined by the vanishing of either the diagonal of their commutator matrix or its anti-diagonal. We find systems of parameters for the coordinate rings of these two sets and their intersection and show that they are complete intersections. Moreover, we prove that these algebraic sets are F-pure over a field of positive prime characteristic and the algebraic set of pairs of matrices with the zero diagonal commutator is F-regular.
Original language | English |
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Pages (from-to) | 29-50 |
Number of pages | 22 |
Journal | Journal of Algebra |
Volume | 589 |
DOIs | |
Publication status | Published - Jan 1 2022 |
Keywords
- Commutator matrix
- Complete intersection
- F-pure
- F-regular
- System of parameters
ASJC Scopus subject areas
- Algebra and Number Theory