Matrix fields, regular and irregular: A complete fundamental characterization

DOI10.1016/0024-3795(86)90254-5zbMath0606.16011OpenAlexW1965566387MaRDI QIDQ1084478

Jacob T. B. jun. Beard

Publication date: 1986

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(86)90254-5

zbMATH Keywords

minimal polynomialGalois actionalgebra of n\(\times n\) matricesembeddings of fieldsscalar matrices

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Finite rings and finite-dimensional associative algebras (16P10) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Polynomials over finite fields (11T06) Algebraic systems of matrices (15A30) Representation theory of associative rings and algebras (16Gxx)

Related Items (1)

Simple subrings of matrix rings

Cites Work

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• A note on subfields of matrix rings
• Matrix fields over the integers modulo m
• Matrix fields over GF(q)
• Matrix fields over prime fields
• Matrix fields over finite extensions of prime fields
• Structure theorems for radical extensions of fields
• Matrix field extensions
• Computing in GF(q)
• Some Primitive Polynomials of the Third Kind
• On Symmetric Representations of Finite Fields
• The number of matrix fields over GF(q)
• Multiple Kunneth Formulas for Abelian Groups
• A rational canonical form for matrix fields

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