## Tags » Reduced Norm

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

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

Noncommutative Ring Theory Notes

#### 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

Noncommutative Ring Theory Notes