Inversion height in free fields

DOI10.1007/BF01587940zbMath0857.16021MaRDI QIDQ1919132

Christophe Reutenauer

Publication date: 11 March 1997

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

zbMATH Keywords

free algebrasuniversal skew fields of fractionsrational seriesfree fieldsstar heightheight structureinversion height

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Infinite-dimensional and general division rings (16K40) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90)

Related Items (19)

A descent basis for the coinvariant algebra of type \(D\) ⋮ Linearizing the word problem in (some) free fields ⋮ Quasi-symmetric functions and the KP hierarchy ⋮ Computing the inversion height of some embeddings of the free algebra and the free group algebra. ⋮ Dirichlet functions of order \(n\) and parameter \(t\) ⋮ Nonnegative companion matrices and star-height of \(\mathbb{N}\)-rational series ⋮ Matrix coefficient realization theory of noncommutative rational functions ⋮ Michel Fliess and non-commutative formal power series† ⋮ Approximation of Multiple Stochastic Integrals and Its Application to Stochastic Differential Equations ⋮ Free loci of matrix pencils and domains of noncommutative rational functions ⋮ Quasideterminants ⋮ Singular tuples of matrices is not a null cone (and the symmetries of algebraic varieties) ⋮ Operator scaling: theory and applications ⋮ Scattering in quantum dots via noncommutative rational functions ⋮ The universal abelian regular ring ⋮ Lie algebraic computation ⋮ Some non-finitely presented Lie algebras ⋮ On the (co)homology of the partition lattice and the free Lie algebra. ⋮ The inversion height of the free field is infinite.

Cites Work

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• Fields of Fractions for Group Algebras of Free Groups
• A Normal Form in Free Fields
• The loop complexity of pure-group events
• On a question of Eggan
• Embedding Free Algebras in Skew Fields

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