Multiplication of two degree-d < n elements in F_{q^n}[x; σ] costs ilde O(d^{ω_K-1} n) operations over F_q.
Theory of non-commutative polynomials.Annals of Mathematics, 34(3):480–508, 1933
6 Pith papers cite this work. Polarity classification is still indexing.
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Proves degree obstructions for equivalence of generalized Airy operators of the same type and answers Katz's 1987 question.
Characterizes when differential polynomial rings R[t;δ] admit compatible Γ-gradings and proves graded analogues of simplicity, primeness, and Noetherianity theorems.
GSRS and GLRS codes contain GRS subcodes and are distinguishable from random codes via square-code methods when m+1 < k < n - ½(m² + 3m).
SGR-R possesses a canonical set of free generators via shifted twists, endowing it with a Grothendieck structure and enough injectives and projectives, plus a semi-graded Baer's criterion analogue.
Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.
citing papers explorer
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Complexity of Low-Degree Skew Polynomial Multiplication over Finite Fields
Multiplication of two degree-d < n elements in F_{q^n}[x; σ] costs ilde O(d^{ω_K-1} n) operations over F_q.
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The Equivalence Problem for Generalized Airy Operators
Proves degree obstructions for equivalence of generalized Airy operators of the same type and answers Katz's 1987 question.
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Graded differential polynomial rings
Characterizes when differential polynomial rings R[t;δ] admit compatible Γ-gradings and proves graded analogues of simplicity, primeness, and Noetherianity theorems.
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Distinguishers for Skew and Linearized Reed-Solomon Codes
GSRS and GLRS codes contain GRS subcodes and are distinguishable from random codes via square-code methods when m+1 < k < n - ½(m² + 3m).
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On the category of semi-graded modules
SGR-R possesses a canonical set of free generators via shifted twists, endowing it with a Grothendieck structure and enough injectives and projectives, plus a semi-graded Baer's criterion analogue.
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Noncommutative differential geometry of ambiskew polynomial rings
Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.