Arep-Algebras Having Cyclic Quadratic Extensions Necessarily Cyclic?

✍ Scribed by Louis H Rowen

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 184 KB
• Volume: 215
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7734

✦ Synopsis

Albert's candidate for a noncyclic p-algebra of prime degree p is actually seen Ž . to be a p-symbol and thereby cyclic , as a consequence of calculations related to the corestriction down a quadratic extension. More generally, under many circum-Ž . stances which subsume the known case p s 3 , a p-algebra of degree p which becomes cyclic after a quadratic extension of the center already is already cyclic. However, there is a proposed counterexample to this assertion in general, which may be noncyclic algebra for p G 5. ᮊ 1999 Academic Press

In this paper we study the cyclicity of a division algebra D of prime 0