Algebraic sets defined by the commutator matrix
Kadyrsizova Z. Yerlanov M.
1 January 2022Academic Press Inc.
Journal of Algebra
2022#58929 - 50 pp.
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.
Commutator matrix , Complete intersection , F-pure , F-regular , System of parameters
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Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Mathematics, Simon Fraser University, Canada
Department of Mathematics
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
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