Amnon Yekutieli and James J. Zhang

Let $D$ be a division algebra over a base field $k$. The homological transcendence degree of $D$, denoted by $\text{Htr}\; D$, is defined to be the injective dimension of the algebra $D \otimes_k D^{\circ}$. We show that $\text{Htr}$ has several useful properties which the classical transcendence degree has. We extend some results of Resco, Rosenberg, Schofield and Stafford, and compute $\text{Htr}$ for several classes of division algebras. The main tool for the computation is Van den Bergh's rigid dualizing complex.

2000 Mathematics Subject Classification: 16A39, 16K40, 16E10.

E-mail:
amyekut@math.bgu.ac.il
zhang@math.washington.edu