The artin-schofield theorem and some applications

DOI10.1080/00927878608823375zbMath0601.16014OpenAlexW2142290163MaRDI QIDQ3735890

Lieven Le Bruyn

Publication date: 1986

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927878608823375

zbMATH Keywords

free algebraring of invariantsirreducible representationsfinite-dimensional representationsmaximal orderfixed ringtrace ringring of generic matricesArtin-Schofield theorem

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Endomorphism rings; matrix rings (16S50) Vector and tensor algebra, theory of invariants (15A72) Representation theory of associative rings and algebras (16Gxx) Rings with polynomial identity (16Rxx)

Related Items (4)

Group actions on central simple algebras: a geometric approach. ⋮ Matrix invariants and complete intersections ⋮ Normalizing elements of the trace ring of generic matrices ⋮ On automorphisms of matrix invariants induced from the trace ring

Cites Work

• Unnamed Item
• Invariants and the ring of generic matrices
• Integral ring homomorphisms
• Reflexive modules and algebra class groups over noetherian integrally closed domains
• Finite dimensional representations of algebras
• The invariant theory of \(n\times n\) matrices
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• Algebraic invariants for a set of matrices
• On Azumaya algebras and finite dimensional representations of rings

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