Forms permitting composition

✍ Scribed by R.D Schafer

• Book ID: 102978351
• Publisher: Elsevier Science
• Year: 1970
• Tongue: English
• Weight: 987 KB
• Volume: 4
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(70)90019-8

✦ Synopsis

In this paper we report, in elementary terms, on the old problem of forms permitting composition, that is, forms N on an algebra which satisfy N(a6) = N(a) N(b), and how this problem has been generalized and completely solved in recent work by K. McCrimmon.

$1. Let F be any field. We denote by F, the associative algebra of all m x m matrices a = (aii) with elements in F:

The algebra F,, has dimension m2 over F.