Triangulations of projective modules

Details Triangulations of projective modules Triangulations of projective modules

2007-04-26

arxiv.org/abs/0704.3633v1

Mathematics

Commutative Algebra

15 pages

Scientific paper

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.

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