2010/01/06 by Mark Hovey, Keir Lockridge, Hovey, Mark +1
Mathematics · #16E10 #18E30 #55P43 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.AT #math.RA #msc:16E10 #msc:18E30 #msc:55P43
paper · pdf · doi:10.48550/arxiv.1001.0902
16 pages
arxiv created 2010/01/06 · arxiv updated 2010/01/14
We define homological dimensions for S-algebras, the generalized rings that arise in algebraic topology. We compute the homological dimensions of a number of examples, and establish some basic properties. The most difficult computation is the global dimension of real K-theory KO and its connective version ko at the prime 2. We show that the global dimension of KO is 1, 2, or 3, and the global dimension of ko is 4 or 5.