Topic
Division ring
About: Division ring is a research topic. Over the lifetime, 1026 publications have been published within this topic receiving 11144 citations. The topic is also known as: skew field & Division ring.
Papers published on a yearly basis
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Papers
Book•
21 Oct 1996
TL;DR: Skew Polynomials and Division Algebras are used in the Brauer Factor Sets and Noether Factor Sets as mentioned in this paper, as well as Galois Descent and Generic Splitting Fields.
Abstract: Skew Polynomials and Division Algebras.- Brauer Factor Sets and Noether Factor Sets.- Galois Descent and Generic Splitting Fields.- p-Algebras.- Simple Algebras with Involution.
343 citations
Book•
25 May 2004
TL;DR: Drensky as mentioned in this paper showed that every PI-ring Satisfies a Power of the Standard Identity of the PI-algebras and every PI ring satisfies a power of the standard identity.
Abstract: A Combinatorial Aspects in PI-Rings.- Vesselin Drensky.- 1 Basic Properties of PI-algebras.- 2 Quantitative Approach to PI-algebras.- 3 The Amitsur-Levitzki Theorem.- 4 Central Polynomials for Matrices.- 5 Invariant Theory of Matrices.- 6 The Nagata-Higman Theorem.- 7 The Shirshov Theorem for Finitely Generated PI-algebras.- 8 Growth of Codimensions of PI-algebras.- B Polynomial Identity Rings.- Edward Formanek.- 1 Polynomial Identities.- 2 The Amitsur-Levitzki Theorem.- 3 Central Polynomials.- 4 Kaplansky's Theorem.- 5 Theorems of Amitsur and Levitzki on Radicals.- 6 Posner's Theorem.- 7 Every PI-ring Satisfies a Power of the Standard Identity.- 8 Azumaya Algebras.- 9 Artin's Theorem.- 10 Chain Conditions.- 11 Hilbert and Jacobson PI-Rings.- 12 The Ring of Generic Matrices.- 13 The Generic Division Ring of Two 2 x 2 Generic Matrices.- 14 The Center of the Generic Division Ring.- 15 Is the Center of the Generic Division Ring a Rational Function Field?.
192 citations
TL;DR: The basic facts on skew polynomials in the (S, D)-setting are developed, the evaluation of such polynomial ring K is defined, and the all-important “Product Theorem” is proved.
167 citations
165 citations
TL;DR: Cauchon et al. as discussed by the authors constructed the derivative-elimination algorithm, which consists of a sequence of changes of variables inside the division ring F=Fract(R), starting with the indeterminates (X1, X2, XN) and terminating with new variables (T1, T1, N) to generate some quantum-affine space R such that F= Fract(R ).
135 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 4 |
| 2024 | 16 |
| 2023 | 13 |
| 2022 | 22 |
| 2021 | 24 |
| 2020 | 30 |