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A note on Amitsur's noncrossed product theorem

Mehran Motiee

Abstract

In this note we give a short and elementary proof for a part of Amitsur's noncrossed product theorem. Our approach does not rely on well-known results of valuation theory. Instead, we employ some preliminary properties of the unit groups of formal iterated Laurent series division rings.

A note on Amitsur's noncrossed product theorem

Abstract

In this note we give a short and elementary proof for a part of Amitsur's noncrossed product theorem. Our approach does not rely on well-known results of valuation theory. Instead, we employ some preliminary properties of the unit groups of formal iterated Laurent series division rings.
Paper Structure (4 theorems, 10 equations)

This paper contains 4 theorems, 10 equations.

Key Result

Theorem 1

If $UD(k,n)$ is a $G$-crossed product, then every division algebra of degree $n$ whose center contains a subfield isomorphic to $k$ is also a $G$-crossed product.

Theorems & Definitions (7)

  • Theorem 1
  • Lemma 2
  • proof
  • Corollary 3
  • proof
  • Theorem 4
  • proof