Some Classes of Multiplicative Forms of Higher Degree

Abstract

Several notions of multiplicativity are introduced for forms of degree d ≥ 3 over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions restricting the structure of a strongly multiplicative form are found.

Key Words:

• Forms of higher degree
• Homogeneous polynomials
• Multiplicative forms
• Strongly multiplicative forms

2000 Mathematics Subject Classification:

• Primary 11E76
• Secondary 11E04
• 12E05

ACKNOWLEDGMENTS

The author would like to acknowledge the support of the the “Georg–Thieme–Gedächtnisstiftung” (Deutsche Forschungsgemeinschaft) during her stay at the University of Trento in 2006/07, and to thank the Department of Mathematics of the University of Trento for its hospitality. She would also like to thank the referee for his or her comments and suggestions, which greatly helped to improve the article.

Notes

Communicated by Susanne Pumplün.