Length complexity of tensor products

2009/03/03 by Wolmer V Vasconcelos, Vasconcelos, Wolmer V
Mathematics · #13D07 #13D30 #13H10 #13H15 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D07 #msc:13D30 #msc:13H10 #msc:13H15

paper · pdf · doi:10.48550/arxiv.0903.0647

17 pages

arxiv created 2009/03/03 · arxiv updated 2009/12/01

Abstract

In this paper we introduce techniques to gauge the torsion of the tensor product A⊗_RB of two finitely generated modules over a Noetherian ring R. The outlook is very different from the study of the rigidity of Tor carried out in the work of Auslander and other authors. Here the emphasis in on the search for bounds for the torsion part of A⊗_R B in terms of global invariants of A and of B in special classes of modules: vector bundles and modules of dimension at most three.

Related

• Torsion and Tensor Products Over Domains and Specializations to Semigroup Rings
• Torsion in tensor products, and tensor powers, of modules
• Torsion in tensor powers of modules
• Finite support of tensor products
• Serre's condition for tensor products and n-Tor-rigidity of modules