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On the projective dimension of tensor products of modules
- Publication Year :
- 2023
-
Abstract
- In this paper we consider a question of Roger Wiegand, which is about tensor products of finitely generated modules that have finite projective dimension over commutative Noetherian rings. We construct modules of infinite projective dimension (and of infinite Gorenstein dimension) whose tensor products have finite projective dimension. Furthermore we determine nontrivial conditions under which such examples cannot occur. For example we prove that, if the tensor product of two nonzero modules, at least one of which is totally reflexive (or equivalently Gorenstein-projective), has finite projective dimension, then both modules in question have finite projective dimension.<br />Comment: 14 pages
- Subjects :
- Mathematics - Commutative Algebra
13D07 (Primary) 13H10, 13D05, 13C12 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2304.04490
- Document Type :
- Working Paper