Media type: E-Article Title: Indecomposable division algebras Contributor: Sethuraman, B. A. imprint: American Mathematical Society (AMS), 1992 Published in: Proceedings of the American Mathematical Society Language: English DOI: 10.1090/s0002-9939-1992-1073530-5 ISSN: 0002-9939; 1088-6826 Keywords: Applied Mathematics ; General Mathematics Origination: Footnote: Description: <p>We present a direct construction of indecomposable division algebras of all indices <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p Superscript n"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{p^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and exponents <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p Superscript m Baseline left-parenthesis n greater-than-or-equal-to m greater-than-or-equal-to 2 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>p</mml:mi> <mml:mi>m</mml:mi> </mml:msup> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mi>m</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">{p^m}(n \geq m \geq 2)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that does not rely on generic methods.</p> Access State: Open Access