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Comments on Shirshov’s Height Theorem

  • Alexander Kemer
Part of the Contemporary Mathematicians book series (CM)

Abstract

In 1941 A.G. Kurosh [1] posed the problem: Is every finitely-generated algebraic associative algebra finite-dimensional? In 1964 E.S. Golod and I.R. Shafarevich 2, 3] constructed a counterexample: they presented an infinite-dimensional finitely-generated nil-algebra. This counterexample shows that in general finitelygenerated algebraic associative algebras are very far from being finite-dimensional.

Keywords

English Transl Commutative Ring Associative Algebra Characteristic Zero Matrix Algebra 
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© Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland 2009

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  • Alexander Kemer

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