Abstract
Albert's candidate for a noncyclic p-algebra of prime degree p is actually seen 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 circumstances (which subsume the known case p = 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 ≥ 5.
| Original language | English |
|---|---|
| Pages (from-to) | 205-228 |
| Number of pages | 24 |
| Journal | Journal of Algebra |
| Volume | 215 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 May 1999 |
Bibliographical note
Funding Information:* Research supported in part by U.S.—Israel Binational Science Foundation Grant 92-00255r1. The author thanks David Saltman for many helpful conversations. Also the author thanks Pascal Mammone for finding a significant error in an earlier version of this paper, which in fact led to the proposed counterexample.