HOMOLOGICAL TRANSCENDENCE DEGREE
2006 ◽
Vol 93
(1)
◽
pp. 105-137
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Keyword(s):
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.
1978 ◽
Vol 30
(01)
◽
pp. 161-163
◽
Keyword(s):
2016 ◽
Vol 2016
(715)
◽
2012 ◽
Vol 190
(1)
◽
pp. 195-211
◽
2012 ◽
Vol 11
(03)
◽
pp. 1250052
◽
Keyword(s):
Keyword(s):
2005 ◽
Vol 2005
(4)
◽
pp. 571-577
◽
2017 ◽
Vol 10
(03)
◽
pp. 1750048