Frobenius Singularities of Algebraic Sets of Matrices
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Date
2019-08-07
Authors
Yerlanov, Madi
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Science and Technology
Abstract
When one studies certain rings, it is natural to classify them according to certain properties. This project focuses on the study of properties of commutative rings associated with algebraic sets. In particular, we consider the algebraic set of pairs of square matrices whose commutator has a zero diagonal. We prove that it is irreducible and F-regular for matrices of all sizes and when the matrix entries are from a eld of positive prime characteristic. In addition, we provide a proof of its F-purity and nd a system of parameters on it. Moreover, we state several conjectures associated to this topic.
Description
Keywords
Frobenius singularities, matrices
Citation
Yerlanov, M. (2019). Frobenius Singularities of Algebraic Sets of Matrices. Nazarbayev University, School of Science and Technology