**Definition**. Let be a division algebra with the center We denote by the additive subgroup of generated by the set Also, we denote by the subgroup of generated by the set… 87 more words

## Tags » Reduced Norm

#### Reduced trace and reduced norm in division algebras

#### Reduced norm and reduced trace (1)

Throughout this post, is a field and is a finite dimensional central simple -algebra of degree

Let and suppose that is the characteristic polynomial of We know from linear algebra that and We also know that is -linear, is multiplicative and for all We’d like to extend the concepts of trace and determinant to any finite dimensional central simple algebra. 195 more words