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The Legacy of Radical Theories in Algebra: From Wedderburn to Köthe

This article explores the impact of radical theories in algebra, tracing the contributions of key figures such as Joseph Wedderburn, Nathan Jacobson, and Jacob Levitzki. We discuss the General and Restricted Burnside Problems formulated by William Burnside, along with Efim Zelmanov's advancements, Shimson Amitsur's results, and the Kurosh Problem laid out by Aleksandr Kurosh. Additionally, we delve into the Köthe Conjecture proposed in 1930 by Gottfried Köthe. This comprehensive analysis highlights the intricate relationships among these mathematical concepts and their historical significance.

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The Legacy of Radical Theories in Algebra: From Wedderburn to Köthe

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  1. Wedderburn’s radical Joseph Wedderburn

  2. Jacobson radical Nathan Jacobson

  3. Levitzki’s and Baer’s radicals Jacob Levitzki

  4. Golod-Shafarevich algebras Igor Shafarevich

  5. General Burnside Problem William Burnside

  6. William Burnside

  7. Restricted Burnside Problem Efim Zelmanov

  8. Amitsur’s result Shimson Amitsur

  9. Kurosh Problem Aleksandr Kurosh

  10. Lance Small

  11. Köthe Conjecture (1930) Gottfried Köthe with a lady

  12. Carl Faith and his wife Molly

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