Some classes of multiplicative forms of higher degree

TL;DR

This paper introduces various notions of multiplicativity for higher degree forms over fields, provides examples, and establishes conditions that restrict the structure of strongly multiplicative forms.

Contribution

It defines new concepts of multiplicativity for forms of degree d ≥ 3 and explores their properties and structural restrictions.

Findings

Examples of multiplicative and strongly multiplicative forms are provided.

Conditions that restrict the structure of strongly multiplicative forms are established.

New notions of multiplicativity extend understanding of higher degree forms.

Abstract

Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ 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.