English

Forms of higher degree permitting composition

Rings and Algebras 2007-05-23 v1

Abstract

Nondegenerate forms N of degree d on a unital nonassociative algebra A over a ring R which permit composition, i.e., satisfy N(1)=1 and N(xy)=N(x)N(y) for all x,y in A, are studied. These forms were first classified by Schafer over fields of characteristic 0 or >d. We investigate cubic and quartic nondegenerate forms which permit composition over certain rings and curves. Classes of highly degenerate cubic forms N over fields which permit composition are constructed.

Keywords

Cite

@article{arxiv.0705.2522,
  title  = {Forms of higher degree permitting composition},
  author = {S. Pumpluen},
  journal= {arXiv preprint arXiv:0705.2522},
  year   = {2007}
}
R2 v1 2026-06-21T08:29:17.253Z