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Kiyoshi Nakayama
San Francisco Bay Area,United States
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Find Kiyoshi Nakayama's PhoneWho Is Kiyoshi Nakayama?
Kiyoshi Nakayama (δΈε±± ζ£, Nakayama Kiyoshi; March 20, 1915 β October 5, 1959) was a highly influential Japanese mathematician renowned for his profound contributions to modern algebra, particularly in the areas of ring theory, representation theory, and homological algebra. He is most famously associated with Nakayama's Lemma, a fundamental result in commutative algebra with wide-ranging applications in algebraic geometry and number theory. Nakayama was a key figure in the development of mathematics in post-war Japan, holding professorships at Osaka University and later at Nagoya University until his untimely death. His work on Frobenius algebras, quasi-Frobenius rings, and the cohomology of groups has had a lasting impact on the field.
How Did Kiyoshi Nakayama's Career Path Shape Their Journey?
Kiyoshi Nakayama's work history includes a series of influential roles in various companies. Here is a detailed list of his professional journey:
What Are Kiyoshi Nakayama's Key Achievements?
Nakayama's Lemma
A cornerstone result in commutative algebra and module theory, concerning the Jacobson radical of a ring. It provides a crucial tool for proving results about finitely generated modules, especially over local rings, and has extensive applications in algebraic geometry and algebraic number theory.
Contributions to Theory of Frobenius and Quasi-Frobenius Algebras/Rings
Made significant advancements in understanding the structure and properties of Frobenius algebras and quasi-Frobenius rings. These algebraic structures possess strong duality properties and are important in representation theory, algebraic topology, and coding theory.
Pioneering Work in Homological Algebra
Contributed significantly to the early development and application of homological methods in algebra. His research included work on resolutions, Ext and Tor functors, and the cohomology of groups, which are fundamental tools in modern algebra.
Nakayama Conjecture (Representation Theory)
Proposed a conjecture in the representation theory of finite-dimensional algebras relating the dominant dimension of an algebra to it being a self-injective (quasi-Frobenius) algebra. This conjecture spurred considerable research in the field.
What's Kiyoshi Nakayama's Educational Background?
Doctor of Philosophy (Ph.D.), Computer Science
UC Irvine - Year 2011
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Company Overview
TieSetTieSet is an AI company specializing in federated learning and edge AI solutions. They enable organizations to train AI models on decentralized data sources without moving the data, ensuring privacy and security. Their platform helps businesses build and deploy scalable AI applications while maintaining data governance and compliance, particularly for industries like healthcare, finance, and telecommunications.
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