2007/04/26 by Mark Hovey, Hovey, Mark, Keir H. Lockridge +1
Mathematics · #16L60 #18E30 #55P43 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #math.AC #math.AT #math.RT #msc:16L60 #msc:18E30 #msc:55P43
paper · pdf · doi:10.48550/arxiv.0704.3633
15 pages
arxiv created 2007/04/26 · arxiv updated 2009/12/01
We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields and exterior algebras on one generator over a graded field (with a unit in the appropriate degree). We also classify the ungraded commutative rings for which the category of projective modules admits a triangulation with respect to the identity suspension. Applications to two analogues of the generating hypothesis in algebraic topology are given, and we translate our results into the setting of modules over a symmetric ring spectrum or S-algebra.